This is unnatural English. We would not say "...at the karaoke." "...at karaoke" or "...at the karaoke bar (etc.)" would be better.
It sounds fine to me.
Agreed, "the karaoke" is pretty unnatural.
カラオケでたくさんうたいました was not accepted.
Because that means, "I sang a lot at karaoke" you are missing songs in the sentence.
I think "カラオケでたくさんうたいました" should also be accepted as an answer. I don't think it is important to have "歌を" in this sentence.