Smirila sam se. Žao mi je što sam te povrijedila.

Because the past participle agrees with the speaker’s gender.

• smirila sam se = said by a woman
• smirio sam se = said by a man

Croatian past tense uses:

• a form of biti (sam = I am/have in this tense construction)
• plus the past participle, which changes for gender and number.

So the ending -la shows a feminine speaker.

This is the perfect tense of the verb smiriti se.

It is built like this:

• smirila = past participle
• sam = I have / I did auxiliary
• se = reflexive particle

So literally it is something like I calmed myself down, though in natural English it is usually just I calmed down.

Se is the reflexive particle. In this sentence, it is part of the verb smiriti se, which means to calm down.

Without se, smiriti usually means to calm someone/something down.

Compare:

• Smirio sam dijete. = I calmed the child down.
• Smirio sam se. = I calmed down.

So here se does not mean a separate word like English self in a strong way; it is just part of how the verb works.

In Croatian, the auxiliary sam and the reflexive particle se are clitics, which means they usually cannot stand in first position.

That is why Sam se smirila sounds wrong.

A normal order is:

• Smirila sam se.

You may also hear:

• Ja sam se smirila.

This includes the subject ja for emphasis, but it is usually omitted because the verb form already shows the person.

Croatian often drops subject pronouns when they are not needed.

In smirila sam se, the form sam already shows first person singular, and smirila shows the speaker is feminine. So ja is unnecessary unless you want emphasis or contrast.

For example:

• Smirila sam se. = neutral
• Ja sam se smirila. = I calmed down, with extra emphasis

Literally, it is closer to something like It is sorry to me or I have regret, but the natural meaning is:

• I’m sorry
• I regret it

This is a very common Croatian expression. You should learn it as a set phrase.

Its parts are:

• žao = sorry/regretful
• mi = to me
• je = is

So Žao mi je is not built like English I am sorry, even though that is how we translate it.

Because Croatian clitics have a preferred order, and mi normally comes before je.

So the standard phrase is:

• Žao mi je.

Not:

• Žao je mi.

This clitic order is something learners usually just have to get used to by exposure.

Mi is in the dative case.

It means to me.

That is why Žao mi je is literally structured more like It is regrettable to me than I am sorry.

Other examples with the same pattern:

• Hladno mi je. = I’m cold.
• Dosadno mi je. = I’m bored.
• Drago mi je. = I’m glad / pleased to meet you

Here što means that in the sense of introducing the reason for the regret.

So:

• Žao mi je što sam te povrijedila. = I’m sorry that I hurt you.

This use of što is very common after expressions of emotion, regret, or evaluation.

After žao mi je, Croatian normally uses što when introducing the thing you regret.

So the natural sentence is:

• Žao mi je što sam te povrijedila.

Using da here would not be the normal choice.

A good learner rule is:

• after žao mi je, use što

Because the second sentence contains a new clause with its own verb phrase in the past tense:

• što sam te povrijedila

That clause means that I hurt you, and it needs its own auxiliary sam.

So you have:

1. Smirila sam se.
2. Žao mi je što sam te povrijedila.

Each past-tense clause needs its own auxiliary.

Te means you and is the accusative singular form of ti.

It is used because povrijediti takes a direct object:

• povrijedila sam te = I hurt you

Compare some pronoun forms:

• ti = you
• te / тебя equivalent as object = you
• ti also appears as dative in some contexts, but here te is clearly the direct object

Povrijediti often means to hurt in either a physical or emotional sense, depending on context.

• povrijediti nekoga = to hurt someone
• uvrijediti nekoga = to offend someone / insult someone

So if the intended meaning is emotional hurt, povrijedila is still possible and very natural.
If you specifically wanted to say offended/insulted, then uvrijedila would be more precise.

For the same reason as smirila: it agrees with the female speaker.

• povrijedila sam = said by a woman
• povrijedio sam = said by a man

Croatian past participles consistently show gender in the singular.

Both sam and te are clitics, and Croatian has a usual clitic order.

In this kind of clause, the standard order is:

• što sam te povrijedila

not usually:

• što te sam povrijedila

A useful practical rule is that the auxiliary like sam tends to come before object clitics like te in these clusters.

You might hear something like that in some contexts, but it changes the structure and is less standard for this exact meaning.

• Žao mi je što sam te povrijedila = I’m sorry that I hurt you
• Žao mi je jer... would sound more like I’m sorry because..., which is a different relationship

After žao mi je, što is the normal and safest choice when saying what you are sorry about.

In most everyday contexts, it is simply:

• I calmed down

Croatian perfect tense often corresponds to the English simple past.
Sometimes English present perfect may fit depending on context, but learners should usually translate it as simple past unless the situation strongly suggests otherwise.

Yes, they sound natural together.

• Smirila sam se. suggests the speaker is no longer emotionally upset.
• Žao mi je što sam te povrijedila. gives the apology or regret.

Together, they create a very natural sequence: first the speaker says she has calmed down, then she apologizes for hurting the other person.