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 their mind at the turn of the New Year, when they sat top of the table.
The German centre-back said heavy losses on the road to Liverpool (5-1), Chelsea (6-0) and Manchester City (6-3, in December) cost Arsenal their 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 their thrashings away to their title rivals will hold them in good stead heading into 2014-15, and also for their 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."
