While the 0-0 stalemate at the Etihad Stadium was a positive start for Inter in the revamped competition, Inzaghi felt his team could have secured victory.
"The players did really well, we knew the quality of our opponents, but we worked well and could have hurt them more in some situations," Inzaghi told Amazon Prime Video Italia.
"In the final third we need to show skill and technique, which we do have in the squad.
"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."
Midfielder Hakan Calhanoglu said Inter were determined not to be intimidated by City who beat them in the 2023 Champions League final.
"We wanted to show that we are not scared to play here. We play football the way they do, with sacrifice we showed that we can also play football," Calhanoglu said.
"We enjoyed ourselves against a very strong team and could also have won, but with the right courage and spirit of sacrifice, we proved that we can compete against anyone."
Inter will now turn their focus to the Derby della Madonnina against AC Milan at home on Sunday.
"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," Inzaghi said.