Sergio Aguero swooped for an injury-time winner on Tuesday night.
Barry said: "We knew we really had to get the three points.
"We fought right to the end and you can't really beat a last-minute winner, so it was a good feeling in the dressing room.
"It was similar to when we played Napoli at home. They are good in possession and counter attack quickly.
"We are still learning in the Champions League and it is such a tough group.
"This has lifted everyone. We knew three points were vital to go on and qualify from the group but this is just the start.
"It is a massive lift but we have just got to build on it."