Prošli mjesec nisam potrošila cijelu plaću, pa sam napokon uspjela nešto uštedjeti.

That ending shows the speaker is female. In Croatian past tense, the active past participle agrees with the subject’s gender and number.

So here:

• potrošila = a woman says spent
• uspjela = a woman says managed/succeeded

If the speaker were male, it would be:

• nisam potrošio
• uspio sam

Croatian often leaves out subject pronouns when they are already clear from the verb form. The forms nisam and sam, together with potrošila / uspjela, already show that the subject is I.

So ja is not necessary here. You could add ja for emphasis, but the neutral version usually omits it.

Croatian past tense is built with:

• a form of biti = to be
• plus the past participle

In the positive, you get sam uspjela. In the negative, ne attaches to the auxiliary, so sam becomes nisam.

So:

• sam potrošila = I spent
• nisam potrošila = I didn’t spend

You do not say ne sam potrošila.

Prošli mjesec is an accusative time expression meaning last month. Croatian often uses the accusative this way for time.

Because mjesec is a masculine inanimate noun, its nominative and accusative singular look the same:

• nominative: prošli mjesec
• accusative: prošli mjesec

You may also hear prošlog mjeseca, which is genitive and is also very common. In everyday use, both can mean last month.

Because this is the direct object of potrošiti, so it has to be in the accusative.

The noun is:

• nominative: plaća = salary
• accusative: plaću

The adjective has to agree with it:

• nominative: cijela plaća
• accusative: cijelu plaću

So cijelu plaću means the whole salary as the thing being spent.

Here pa means something like so, and so, or therefore. It connects the first part with the result that follows.

So the logic is:

• I didn’t spend my whole salary
• so I finally managed to save something

It is not just a simple and here; it shows consequence.

Croatian short unstressed words such as sam usually appear very early in the clause. That is why sam comes before longer stressed words like napokon and uspjela.

So pa sam napokon uspjela is the natural neutral order. If you said pa ja sam..., that would add emphasis to ja.

Uspjela nešto uštedjeti means managed to save something. It adds the idea that saving money was difficult, unusual, or had not happened before.

If you say napokon sam nešto uštedjela, it simply means I finally saved something. That is also possible, but it does not stress the idea of managing to do it as strongly.

This is mainly about aspect.

• potrošiti is perfective: to spend up, to use up completely
• trošiti is imperfective: to spend, to be spending, to spend habitually

Because the sentence is about whether the whole salary was fully spent, potrošiti is the natural choice: nisam potrošila cijelu plaću = I didn’t spend up the whole salary.

Likewise:

• uštedjeti is perfective: to save some amount successfully
• štedjeti is imperfective: to save money in general, to be saving, to economize

So nešto uštedjeti focuses on the achieved result.

Nešto means something or some amount. In this sentence, it naturally means some money.

Croatian often leaves novca unspoken when the context is obvious. So:

• nešto uštedjeti = save something / save some money
• nešto novca uštedjeti = save some money

Both are possible, but the shorter version sounds very natural.

Napokon means finally or at last. It adds a feeling that this result took some time or effort.

It is very close to konačno, and in many sentences they can replace each other. Very roughly:

• napokon often feels a bit like at last
• konačno can sound a bit more neutral, like finally

So napokon uspjela suggests a sense of relief or achievement.

Yes, it can. Croatian word order is fairly flexible, so you could also say:

• Napokon sam uspjela nešto uštedjeti.
• Pa sam uspjela napokon nešto uštedjeti.

But the short auxiliary sam still tends to stay near the beginning of its clause. The original order sounds very natural and balanced.