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.
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."
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.
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."
Source: PA
Source: PA