После разговора мне пришлось признать, что я был неправ.

Because после requires the genitive case.

• разговор = conversation (dictionary form, nominative)
• разговора = genitive singular

So:

• после разговора = after the conversation

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после встречи = after the meeting

So the ending -а here is not random; it shows the noun is in the genitive after после.

Мне пришлось means something like I had to or it turned out that I had to.

Literally, the construction is impersonal. Russian often expresses necessity this way:

• мне пришлось = to me, it became necessary / fell to me
• natural English: I had to

The pronoun is in the dative because the experience or necessity is happening to the person:

• мне пришлось = I had to
• ему пришлось = he had to
• нам пришлось = we had to

This is a very common structure in Russian.

Because пришлось is used in an impersonal construction.

In this sentence, пришлось does not agree with я. It acts like a neutral impersonal predicate, so it appears in the neuter singular past form:

• пришлось

This is normal in Russian with verbs like пришлось, удалось, получилось, необходимо было, etc.

So even though the meaning is I had to, the grammar is closer to:

• мне пришлось признать = it was necessary for me to admit

That is why you do not get a masculine/feminine/plural form agreeing with the speaker.

Both can sometimes translate as had to, but they are not used in exactly the same way.

мне пришлось

This often means:

• circumstances forced it
• it ended up being necessary
• I had no real choice

It often sounds more like I ended up having to or I was forced to.

я должен был

This often means:

• obligation
• duty
• what was expected
• what one was supposed to do

So:

• Мне пришлось признать... = I had to admit... / I ended up having to admit...
• Я должен был признать... = I was supposed to admit... / I ought to have admitted...

In your sentence, пришлось sounds very natural because the idea is that after the conversation, the speaker was compelled by the situation to admit being wrong.

Because признать is the perfective form, and here the speaker means a single completed act of admitting something.

• признавать = imperfective, process / repeated / general
• признать = perfective, one completed admission

In this sentence:

• мне пришлось признать = I had to admit

The focus is on the result: the speaker did in fact come to that admission.

Compare:

• Он не любит признавать ошибки. = He does not like admitting mistakes.
  (general habit/process)
• Он наконец признал ошибку. = He finally admitted the mistake.
  (completed act)

Что introduces a subordinate clause, here meaning that.

So the structure is:

• мне пришлось признать = I had to admit
• что я был неправ = that I was wrong

Together:

• мне пришлось признать, что я был неправ = I had to admit that I was wrong

In English, that can often be omitted:

• I had to admit that I was wrong
• I had to admit I was wrong

In Russian, что is normally kept in this kind of sentence.

Because the sentence refers to a situation in the past.

• я неправ = I am wrong
• я был неправ = I was wrong

In Russian, the verb to be is usually omitted in the present tense:

• Я неправ. = I am wrong.

But in the past tense, Russian uses forms of быть:

• Я был неправ. = I was wrong.
• Она была права. = She was right.

So был is necessary here because the speaker is talking about being wrong at that earlier time.

Неправ means wrong in the sense of not being right in an argument, judgment, or opinion.

It is a short-form adjective/predicative form, and it is very common after pronouns or nouns when talking about who was right or wrong:

• Я неправ. = I am wrong.
• Ты неправ. = You are wrong.
• Она права. = She is right.

неправильный

This usually means incorrect, wrong, not correct in a more descriptive sense, for example:

• неправильный ответ = an incorrect answer
• неправильное произношение = incorrect pronunciation

So:

• я был неправ = I was wrong
• это был неправильный ответ = that was an incorrect answer

Yes, it comes from an adjective, but here it is the short form.

Russian has:

• long forms of adjectives, often used before nouns or in fuller descriptions
• short forms, often used as predicates after the subject

Here:

• неправ = short form, masculine singular
• feminine: неправа
• neuter: неправо
• plural: неправы

Examples:

• Я неправ.
• Она неправа.
• Они неправы.

This is one of the most common uses of short-form adjectives in everyday Russian.

You actually can omit я in some contexts, because Russian often leaves out pronouns when they are clear from the situation.

So both are possible:

• ...что я был неправ
• ...что был неправ

But including я is very natural here and can make the clause clearer or slightly more explicit.

Russian pronouns are often omitted less automatically than in Spanish or Italian; whether they appear can depend on style, clarity, and emphasis.

It sets the time context: after the conversation.

Russian often puts time expressions at the beginning of a sentence to frame what follows:

• После разговора мне пришлось признать...
• Вчера я понял...
• После ужина мы ушли...

This word order is natural because it tells the listener first when the realization happened.

If you changed the order, the meaning would stay the same:

• Мне пришлось признать после разговора, что я был неправ.

But the original sentence sounds smoother and more natural because the time phrase is introduced first.

Yes. Разговор is a flexible word.

Depending on context, it can mean:

• conversation
• talk
• discussion

In your sentence, после разговора could be understood as:

• after the conversation
• after the talk
• after speaking with someone

Conversation is probably the safest neutral translation, but the exact English word depends on context and tone.

Because Russian normally separates subordinate clauses with a comma.

Here the main clause is:

• мне пришлось признать

And the subordinate clause is:

• что я был неправ

Russian punctuation is stricter than English in this area. When a clause is introduced by что, a comma is usually required:

• Я знаю, что он прав.
• Она сказала, что придёт.
• Мне пришлось признать, что я был неправ.

So the comma here is standard Russian punctuation.

It sounds neutral and natural. It is a normal way to say:

• After the conversation, I had to admit that I was wrong.

It is not especially formal, but it is a little more polished than very casual speech because of мне пришлось признать.

More casual alternatives might include things like:

• После разговора я понял, что был неправ.
  = After the conversation, I realized I was wrong.

But your sentence is completely normal in both spoken and written Russian.

Yes, very often.

Because of мне пришлось признать, the sentence can suggest:

• the speaker did not want to admit it
• but the facts or the conversation forced that conclusion

So it often carries a shade of:

• I had to admit it, whether I liked it or not

That nuance is one reason пришлось works so well here. It is stronger than a simple neutral statement like:

• Я признал, что был неправ. = I admitted that I was wrong.

With пришлось, there is often a feeling of reluctant necessity.