"It is a shame that I did not put on a tie."
Translation:Il est dommage que je n'aie pas mis de cravate.
Yes, it's because its being used negatively. As in "I didn't put on any tie." It's -J'ai une cravate- but -je n'ai pas de cravate-. https://www.duolingo.com/comment/20943463/Il-est-dommage-que-je-n-aie-pas-mis-de-cravate
I think that the indefinite article un/une changes to de in a negative sentence. See https://french.kwiziq.com/revision/grammar/un-and-une-become-de-or-d-in-negative-sentences-indefinite-article and https://www.lawlessfrench.com/grammar/de-vs-du-de-la-des-articles/.
I'm not a francophone, but this reads to me as an informal abbreviation of C'est dommage que... / Il est dommage que..., and so it doesn't quite match the tone of the original.
If the English sentence had been simply "Shame I didn't put on a tie.", then I think it would be a perfect translation.
Surprising really since both Collins and Larousse offer C'est dommage que for it's a shame/pity that. See: