Smanjili smo trošak.

Because Serbian forms this past tense with two parts:

• smanjili = the past participle of smanjiti
• smo = we are, used here as the auxiliary have-type element in the past tense

Together, smanjili smo means we reduced.

This is the Serbian perfect tense, which is the normal way to talk about past actions:

• smanjili smo = we reduced / we have reduced

The dictionary form is smanjiti, which means to reduce / to decrease / to lower.

So:

• smanjiti = infinitive
• smanjili smo = we reduced

Also, smanjiti is a perfective verb, so it usually suggests a completed action with a result.

That ending shows agreement with the subject in number and sometimes gender.

Here, smanjili is the masculine plural form. With mi (we), Serbian often uses:

• smanjili smo = used for a group of men, a mixed group, or when gender is not being specified
• smanjile smo = if the speakers are all female

So if a group of women said this, they would normally say:

• Smanjile smo trošak.

Because Serbian often omits subject pronouns when they are already clear from the verb form.

In smanjili smo, the word smo already tells you the subject is we.

So both are possible:

• Smanjili smo trošak.
• Mi smo smanjili trošak.

The version without mi is very normal and natural.

Because smo is a clitic. In Serbian, clitics usually come in the second position of the sentence or clause.

So:

• Smanjili smo trošak. = natural
• Mi smo smanjili trošak. = also natural
• Trošak smo smanjili. = also possible, with emphasis on trošak

But:

• Smo smanjili trošak. = not normal as a neutral sentence

So the auxiliary smo usually cannot just stand at the very beginning by itself.

Because trošak is the direct object of the verb smanjiti, and that means it should be in the accusative.

However, trošak is a masculine inanimate noun, and for masculine inanimate nouns, the accusative singular is often the same as the nominative singular.

So:

• nominative: trošak
• accusative: trošak

That is why the form does not visibly change here.

Trošak means cost or expense.

Depending on context, the sentence can mean things like:

• We reduced the cost.
• We reduced the expense.
• We lowered costs (if the context is talking about one specific cost category)

A related plural form is:

• troškovi = costs / expenses

So you may also hear:

• Smanjili smo troškove. = We reduced the costs / expenses.

This is about aspect, which is very important in Serbian.

• smanjiti = perfective → a completed reduction
• smanjivati = imperfective → ongoing, repeated, or habitual reducing

So:

• Smanjili smo trošak. = We reduced the cost.
  (the action is viewed as completed)

Compare:

• Smanjivali smo troškove. = We were reducing / used to reduce costs.

In your sentence, the speaker is presenting the reduction as a finished result.

Yes. That is completely correct.

The difference is mainly emphasis:

• Smanjili smo trošak. = neutral
• Mi smo smanjili trošak. = emphasizes we
• Trošak smo smanjili. = emphasizes the cost

So the words can move around more than in English, but the clitic smo still has to follow the first stressed element.

No. Serbian does not have articles like a and the.

So trošak can mean:

• a cost
• the cost

The exact meaning comes from the context.

That is why Smanjili smo trošak can naturally be translated as We reduced the cost even though there is no separate word for the.

A rough English-friendly guide is:

• Smanjili ≈ smah-NYEE-lee
• smo ≈ smo
• trošak ≈ TRO-shak

A few notes:

• nj sounds like the ny in canyon
• š sounds like sh
• the r in Serbian is usually tapped or rolled more than in English

So the whole sentence is roughly:

smah-NYEE-lee smo TRO-shak

Yes. In many contexts, reduced, lowered, or decreased can all work.

The verb smanjiti is quite flexible and often corresponds to:

• reduce
• decrease
• lower

The best English translation depends on context, but the Serbian grammar stays the same.