Наша команда проиграла игру.

Because наша has to agree with команда.

In Russian, possessive words like наш (our) change form for gender, number, and case, much like adjectives do. Since команда is:

• feminine
• singular
• nominative

the correct form is наша.

So:

• наш = masculine singular
• наша = feminine singular
• наше = neuter singular
• наши = plural

Because команда is feminine, you say наша команда.

Because Russian grammatical gender is about the noun, not the real-life sex of the people involved.

Команда is a grammatically feminine noun. That is why other words agreeing with it also take feminine forms:

• наша команда
• команда проиграла

This does not mean the team is female. It just means the noun команда belongs to the feminine grammatical class.

A big clue is the ending -а. Many Russian nouns ending in -а / -я are feminine.

In the Russian past tense, verbs agree with the subject in gender and number.

The subject here is команда, which is feminine singular, so the past tense verb is feminine singular too:

• masculine: проиграл
• feminine: проиграла
• neuter: проиграло
• plural: проиграли

So Наша команда проиграла is literally structured as Our team lost, with the verb marked as feminine because команда is feminine.

Because игру is in the accusative case, which is used here for the direct object of the verb.

The basic dictionary form is игра. But after a transitive verb like проиграть when you mean lose a game, Russian uses the direct object:

• nominative: игра
• accusative: игру

For many feminine nouns ending in -а, the accusative singular changes -а to -у.

So:

• игра = the game, as a subject
• игру = the game, as an object

Here is the grammatical breakdown:

• наша — nominative, feminine, singular
• команда — nominative, feminine, singular
• проиграла — past tense verb, feminine, singular
• игру — accusative, feminine, singular

Why these cases?

• Наша команда is the subject, so it is in the nominative
• игру is the direct object, so it is in the accusative

Because Russian does not have articles like a or the.

So Наша команда проиграла игру can correspond to English with an article supplied from context, such as:

• Our team lost the game
• sometimes even Our team lost a game, depending on context

Russian leaves that distinction unstated unless something else in the sentence makes it clear.

Проиграла is the perfective past tense of проиграть.

Perfective aspect presents the action as a completed whole. That fits very naturally with a finished event like losing a game.

So Наша команда проиграла игру means the loss happened and is viewed as complete.

If you used проигрывала, that would be the imperfective past:

• проигрывала can mean was losing, used to lose, or lost repeatedly, depending on context

For example:

• Наша команда часто проигрывала игры. = Our team often lost games.
• В тот момент наша команда проигрывала. = At that moment our team was losing.

So for one completed game, проиграла is the normal choice.

Yes. Russian word order is much more flexible than English word order.

The neutral, straightforward order here is:

• Наша команда проиграла игру.

But other orders are possible if you want to change emphasis:

• Игру проиграла наша команда.
  Emphasis on who lost the game.
• Наша команда игру проиграла.
  Can sound contrastive, as if correcting or highlighting the game.

Even though the order can change, the cases still show who did what:

• команда is the subject
• игру is the object

Yes. That is a perfectly natural sentence.

It simply means:

• Our team lost

You do not have to mention игру if the context already makes it clear what was lost. Russian often leaves out an object when it is obvious or unimportant.

So both are fine:

• Наша команда проиграла.
• Наша команда проиграла игру.

The second is just more explicit.

Not always. Проиграть can be used in a couple of common patterns.

1. проиграть что? — to lose something, especially a game/match

   • проиграть игру
   • проиграть матч

2. проиграть кому? — to lose to someone

   • проиграть сопернику = to lose to the opponent

So Russian can express either:

• what was lost
• to whom someone lost

Sometimes context makes only one of these necessary.

The standard stress is:

• На́ша кома́нда проиграла́ игру́.

Word by word:

• На́ша
• кома́нда
• проиграла́
• игру́

Stress matters in Russian, so it is worth learning words together with their stress patterns.