It was the first time in two years that City hadn't scored in the Champions League at home.
Inzaghi said afterwards: "The lads did really well, we knew the quality of our opponents, but we worked well and could’ve hurt them more in some situations.
“We suffered a little more in the second half, but those Darmian and Mkhitaryan chances could’ve gone in. I congratulated the lads, now we move forward.
"This is the first time we haven’t scored this season and it is something we need to work on.
“Against these sides like Manchester City and Real Madrid, you always seem like you might be able to score a goal, but then they manage to rescue it.
“Taremi did well to pass it to Carlos Augusto and Ederson made a good save. As for Darmian, he said that he heard Barella call for the pass, their defender did well to intercept, otherwise it would’ve been clear on goal.”
Inter next meet AC Milan this weekend.
Inzaghi added: “It will be a derby, we all know what that means for the club and our fans. They never stopped singing tonight in Manchester. We will stay here overnight, fly back tomorrow and try to prepare the match in just a few days.”