Barry felt the weight of expectation after a devastating start to the domestic campaign had played its part, and believes the result may bring a reality check to those who thought City would cut a swathe through Group A against Napoli, Villarreal and European heavyweights Bayern Munich.
"I can imagine the fans and a lot of people were expecting us to go out there and roll over Napoli but it was never going to be like that," Barry said after his first appearance in the competition.
"The Champions League adds a lot of pressure, it is completely on a different level to the Europa League.
"We have probably made that step up - as a squad we have the players who deserve to be playing there - and both teams have a great chance to qualify from the group.
"We were disappointed not to get three points with the chances we created in the first half.
"The first goal is always vital and if we had got that the game would have opened up and suited us more, but it is not always going to happen like that.
"But I enjoyed it. It was a great atmosphere and it was one of the reasons I joined the club. As a team we learned a lot."