The Gunners lost 2-0 to the defending English champions in their Premier League clash.
"If you want to be in the top four you have to compete with Chelsea, Man City, Man United and Tottenham," The Sun quotes the centre-back as saying. "These teams are in this zone. We need to win against those four as much as we can — it is a good point to show how we are.
"We need our character on Sunday [against Chelsea at Stamford Bridge]. "That is the most important thing. In the second half against Manchester City, we showed our character, which was much better than the first half.
"We were a bit scared against Man City from the beginning. We were not that confident. The second half was much better. With a bit of luck we could have scored in two or three situations."
Arsenal are currently sixth in the Premier League table.