The Londoners are on the verge of escaping from the campaign with their UEFA Champions League status intact, despite a strong challenge from Everton pushing them all the way.
Arsene Wenger's men require three more points from their final two games to secure fourth spot, and the qualifying place - although Arsenal had higher honours on its mind at the turn of the New Year, when it sat top of the table.
The German center back said heavy losses on the road to Liverpool (5-1), Chelsea (6-0) and Manchester City (6-3, in December) cost Arsenal its chance.
"Everyone dreamed about the title, but it takes more than staying top until the winter period," Mertesacker said. "We could not afford (to lose) those big games against big teams, so we did not deserve to be in the first three. That is something we have to manage much better next year.
"The away games killed us. We have to learn how to play and how to defend in the first 20 minutes."
Mertesacker felt Arsenal's lessons learnt from thrashings away to title rivals will hold it in good stead heading into 2014-15, and also for the potentially drought-breaking FA Cup final clash against Hull City on May 17.
"Everyone questioned our qualities but the way we have come back, especially from those away games, as a team makes us stronger for the future," he said. "This year, we have struggled heavily with a couple of injuries but we have regrouped very well. Securing Champions League football was another test for us.
"We are in the FA Cup final and it is important to finish in the top four. They are good targets for us now."