watasi ha siken ni hugoukaku datta node, totemo zannen desita.

私 means I, but in Japanese the subject is often omitted when it is already clear from context.

So this sentence could naturally be said as:

試験に不合格だったので、とても残念でした。

Including 私 is not wrong. It just makes the subject explicit, which is common in learner materials and sometimes useful for emphasis or clarity.

は marks 私 as the topic of the sentence.

So 私は means something like:

• as for me
• speaking of me

It does not always mean the same thing as the English subject marker. Here, it sets up the sentence as being about the speaker.

In expressions with 合格 and 不合格, the thing you pass or fail is often marked with に.

So:

• 試験に合格する = to pass an exam
• 試験に不合格だ = to be unsuccessful on an exam / to have failed an exam

You can think of に here as marking the target or event involved.

This is a set pattern, so it is best learned as a chunk:

• N に 合格する
• N に 不合格だ

不合格 is basically a noun, meaning failure or not passing.

But in Japanese, many nouns can function like na-adjectives or combine with the copula だ to describe a state.

So:

• 不合格だ = to be failed / to be unsuccessful
• 不合格だった = was failed / had failed

That is why you see だった after it rather than something like an -i adjective ending.

Both are possible, but they sound a little different in style.

• 不合格だったので uses the plain past before ので
• The main sentence ends politely with 残念でした

This mix is very common in Japanese:

• a plain form inside a clause
• a polite form at the end of the full sentence

So this is perfectly normal:

不合格だったので、残念でした。

You could also say:

不合格でしたので、とても残念でした。

That sounds more formal and more consistently polite.

ので means because or since.

It connects the reason to the result:

• 試験に不合格だったので = because I failed the exam
• とても残念でした = I was very disappointed

Compared with から, ので often sounds:

• a bit softer
• a bit more explanatory
• a bit more objective

So ので is very common when giving reasons politely.

Because both parts refer to something that happened in the past.

• 不合格だった = I had failed / was unsuccessful
• 残念でした = I was disappointed

The first past form describes the reason. The second past form describes the speaker’s feeling after that event.

So the timeline is:

1. the exam result was failure
2. because of that, the speaker felt disappointed

残念 is a na-adjective (or adjectival noun), meaning things like:

• disappointing
• regrettable
• unfortunate

In this sentence, 残念でした means I was disappointed or it was regrettable.

Because it is a na-adjective, it works with です / でした:

• 残念です = it is disappointing / I’m disappointed
• 残念でした = it was disappointing / I was disappointed

とても is an adverb meaning very.

It modifies 残念でした:

• 残念でした = I was disappointed
• とても残念でした = I was very disappointed

This is a very common pattern:

• とても嬉しかった = I was very happy
• とても難しかった = it was very difficult
• とても残念でした = I was very disappointed

Yes, it is understandable and grammatical, but it sounds a little formal or textbook-like.

A more everyday way might be:

• 試験に落ちたので、とても残念でした。
• 試験に落ちて、とてもがっかりしました。

Notes:

• 落ちた literally means fell, but with exams it means failed
• がっかりしました is a very common way to say was disappointed

So your sentence is fine, but in conversation many people would choose 落ちた or がっかりした.

Both can be translated as I was disappointed, but they are not exactly the same.

• 残念でした often has the nuance of it was unfortunate/regrettable
• がっかりしました focuses more directly on the speaker’s emotional reaction of feeling let down

So:

• 試験に不合格だったので、とても残念でした。
  = Because I failed the exam, it was very regrettable / I was very disappointed.

• 試験に落ちたので、とてもがっかりしました。
  = Because I failed the exam, I was very disappointed.

In many everyday situations, がっかりしました sounds a little more personal and emotional.

Yes.

You could:

• leave it out completely: 試験に不合格だったので、とても残念でした。
• replace it with another pronoun or noun if needed:
  • 彼は = as for him
  • 彼女は = as for her
  • 田中さんは = as for Tanaka

Japanese often leaves out subjects when they are obvious, so omission is usually the most natural choice unless the speaker wants emphasis or contrast.