City were denied an early point in Group E when Boateng's well-struck effort from the left side of the area deflected off Mario Gotze and the end result did not sit well with a disappointed Hart who had been at the top of his game prior to the winner.
"We did okay and looked like we were going to get a result out of it, which would have been a good start to the group away against a good side," said the England number one.
"But it was an unfortunate deflection that ended up going in, and that killed us.
"I had a bit to do, but we defended well on the whole and had a few chances. It could have been the perfect performance and we come away with a 1-0 win, but unfortunately we ended up with a loss."
Hart added: "I always seem to have plenty to do when we play in Germany, against good sides, but unfortunately it didn't affect the result.
"I'm not here for headlines - if I was, I would probably have quit. It would have been a good game if we had got the result.
"The only way it would be a good game for me would be if we win the group on goal difference."
City, who sit third on their group table, will now prepare for their Premier League clash with domestic league leaders Chelsea at the Etihad Stadium on Sunday.
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