The visitors put in a solid performance at the Emirates but were undone by goals in either half from Olivier Giroud and Tomas Rosicky.
The loss leaves Everton in 14th place in the Premier League table and with just one win in their last 11 top-flight matches.
“It has been more of a chore than enjoying our football,” said Martinez. “I have not seen that enjoyment in our team in the league with points at stake.
“I do see that enjoyment in the Europa League, but I feel the group is becoming stronger.”
Everton have looked at their best in the Europa League this season and eased into the last 16 of the competition with a 7-2 aggregrate victory over Young Boys in midweek.
But they have struggled in the Premier League and Martinez feels the defeat to Arsenal summed up their campaign.
“You have a 2-0 scoreline, but it doesn’t reflect what happened on the pitch. Unfortunately that is the story of our season,” he said.
“We have not had the momentum that allows you to win games, that is something we need to change quickly.”
Romelu Lukaku and Aaron Lennon went close to levelling the scores at the Emirates but both were denied by saves from David Ospina in the second half.
“I thought we did things pretty well in the first half but we didn???t carry enough intent in our attack,” said Martinez.
“I felt we managed the game well in the way we stopped Arsenal having any threat on the counter which has been one of their biggest threats at home this season. But we should have had a bit more intent.”