The Gunners fell behind shortly before half-time when Joleon Lescott nodded home from a corner after an evenly-contested first half.
But Arsène Wenger’s men, who enjoyed 52 per cent of the possession at the Etihad Stadium, were rewarded for their persistence when Laurent Koscielny drilled home from close range to level eight minutes from time.
“You need to show your character and show that you are ready for the big games,” Mannone, 24, told Arsenal Player.
“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.”
Mannone admitted he was disappointed with himself for Lescott’s goal after the Italian failed to collect the corner after choosing to come off his line.
“I was not happy with the goal obviously but I came back stronger with some saves,” he said.
“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.”
ENHANCED ODDS: Get 7/1 on Man Utd to beat Swansea