The answer of your teacher is not correct. Because the verbe s’amuser is a reflexive verb, in any tense, you cannot omit the reflexive pronoun: in your case, the second nous.

That means your version is correct:

Nous ne nous sommes pas amusés au festival.

Teacher is not correct, indeed: “Nous ne sommes pas amusés au festival.” means “We are not entertained at the festival” (which is in present tense) while your answer “Nous ne nous sommes pas amusés au festival” means “We didnt have fun at the festival”.

Please insist that you have the right answer with your teacher.

I’ll give a little hint in addition to the other answers.

The teacher is indeed wrong.

Nous ne sommes pas amusés au festival

This sentence is not wrong per se, but it does not mean the same thing, as yactouat explained.

It uses a passive form. It is in “présent” tense. Therefore it’s a wrong answer to the exercise (which requires a passé composé).

Nous ne nous sommes pas amusés au festival

This is the right answer, because it actually is in the “passé composé” tense, in the reflexive form as Laurent has explained.