Just to check on the pronunciation of "zgubiliśmy".
Stress appears to be on the THIRD last syllable ("bi"), correct?
This would be a departure from the normal rules of pronunciation (SECOND-last syllable). Is this the case for all these past tense forms with two syllable endings (-liśmy, -liście, -łyśmy, -łyście) ?
They are both correct Genitive variants, even if "nic" does not look very Genitive. Sometimes one will sound better than the other to the native ear, but I am not aware of any rules. Maybe "niczego" is better at the end of the sentence.
"Nic nie zgubiliśmy" is perfectly fine (especially if you were 'accused' of losing sth) and should have worked.