Despite dominating for large parts of the first-half the Gunners found themselves a goal down when Joleon Lescott headed past the Italian, however Laurent Koscielny fired home late on to salvage a hard-fought point.
The keeper insisted that they must be mentally strong when playing the top sides in the league, something he hailed his team for doing against Roberto Mancini's men.
"You need to show your character and show that you are ready for the big games," he told the club's official website.
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"Every team is difficult because there is not such a difference between sides [in the Premier League]. You need to perform well every week and get as many points as you can.
"We did all we could do to put pressure on them. It shows great character to come back, especially against the champions."
The 24-year-old, who is enjoying a run in the first-team after Wojciech Szczesny's injury problems, has been in good form this season but was partially at fault for City's goal when he failed to deal with David Silva's corner.
Mannone was disappointed with his error but suggested that he made up for it with some good saves later on, namely when denying Vincent Kompany and Sergio Aguero, while stating he is pleased to have helped secure the draw.
"I was not happy with the goal obviously but I came back stronger with some saves," he added.
"The team performed really well and everyone gave everything to come back and get a point. Every save that can help the team, I am really happy with."