The Barclays Premier League title-holders have again made a slow start in the elite European competition.
Roberto Mancini's men failed to progress beyond the group stage last year and - in common with 12 months ago - have taken just a point from their opening two games this term.
Their latest frustrating result was a 1-1 draw with German champions Borussia Dortmund, and that could easily have been worse but for the brilliance of Hart and a controversial late Mario Balotelli penalty.
Last season's premature exit, in what was City's first entry into the competition, was largely put down to experience as they went on to win the domestic title but more is expected this time.
Hart said: "I don't know if it is a learning curve - we are in with the big boys now, there is no place to hide.
"There is no point learning if you are not going to win. We need one big game against Ajax next."
City were beaten at Real Madrid in their first game of a tough-looking Group D and their hopes of progress will now hinge on back-to-back games against the Dutch champions.
Mancini feels his team also need to learn quickly to keep their hopes in the competition alive.
The Italian said: "Probably in this moment we are not ready. All these teams we have met - Real Madrid - they are used to playing Champions League every year, they have more experience than us.
"This can change during the competition. Probably we need two or three good results.
"If we understand why we didn't play well, why we did some mistakes - that will be important."
City and Dortmund both had numerous chances in a pulsating first half at the Etihad Stadium but the score remained goalless due to the excellence of both goalkeepers.
While Hart denied Mario Gotze three times and Ilkay Gundogan with world-class stops, opposite number Roman Weidenfeller was equally impressive to save from Sergio Aguero twice and Samir Nasri.
Hart could do little to prevent Marco Reus finally scoring just after the hour following a mistake by Jack Rodwell but retained high standards as Dortmund continued to pound his goal.
There were two further fine saves from Robert Lewandowski - who also put another good chance wide - as well as ones from Gotze and Gundogan.
City were hanging on when Neven Subotic was harshly ruled to have handled in the last minute and substitute Balotelli calmly stepped up to score.
Hart said: "We got a point against one our rivals to qualify from the group and maybe we shouldn't have.
"We've not played great and they have played well and we've come out with a point, hopefully we can move forward with that.
"They're a fantastic team for a pot four side in our group and it shows what a group we're in, what a tough task but you have to enjoy it.
"If we get through we (deserve) a big pat on our back but it's going to be hard."
Hart was modest when asked to reflect on his own performance, which had many including England team-mate Wayne Rooney hailing him as the world's best goalkeeper.
The 25-year-old said: "It's nice to make saves, it is not something I have to do a great deal at City but when required I try to step in and I was required a few times."
Hart is yet to keep a clean sheet for City this season and the defence, a considerable strength last season, has become a concern.
Hart said: "We were pretty open but it allows us to play forward.
"Hopefully we can shore it up again and be the force that we are."