The north London appeared on course for a third successive Premier League victory after in-form Gunners striker Alexis Sanchez had broken the deadlock in the 63rd minute.
However, former Spurs midfielder Gyfli Sigurdsson levelled with a brilliant free-kick before Bafetimbi Gomis scored with his first touch of the game to seal three points.
And Mertesacker, who was part of the side that drew with Anderlecht despite leading 3-0 with a half-hour to go in the Champions League on Tuesday, was critical of Arsenal’s mistakes in the final 15 minutes.
“The game was completely in our hands. But then we have to play serious football and not make mistakes,” Mertesacker told Sky Sports.
“Anderlecht came back at 3-0 and Swansea came back today from one goal. We have potential, but unless we play that serious football any team will punish us.
“We have to play simple. We think we can do some difficult things, but we need to keep possession. After such a setback as Anderlecht we normally bounce back straight away, but we didn’t. We need to work hard on the issues now.”
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