Despite being held by the Toffees, the draw saw Arsenal extend their lead to five points at the top of the table heading into the festive period.
"I think that was the toughest game we have been through the whole season," Mertesacker 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."
Arsenal return to Champions League action on Wednesday when they take on Napoli in Italy.