The Gunners scored first through Mesut Ozil in the 80th minute before Barcelona loanee Gerard Deulofeu responded in fine fashion for the Toffees four minutes later.
The draw left Arsenal on top of the table, five points clear, but Mertesacker felt it was the toughest test of the campaign thus far.
“I think that was the toughest game we have been through the whole season,” he told the club’s official website. “They pressed us high up, all the way through from the start until the end.
“We couldn’t play that much and in the second half everything was possible on both sides, with chances here and there so I think it was a fair result.
“We have tough games coming up over the next week and over the Christmas period. We just want to go one game at a time.
“We are really relaxed, we don’t have to respond to anyone. We just have to do our job every single second of the game. That is our target, nothing else.”
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