Everton, who are 12th in the Premier League table with 28 points from 26 matches, have endured an inconsistent season compared to the previous campaign when they finished fifth.
"It's true that we go into Premier League games with too much responsibility, feeling there's more to lose than to gain," Martinez told a news conference.
"Maybe now is the time to take things one game at a time and try and enjoy our Premier League games."
Martinez's side have enjoyed their Europa League adventure, however, and set up a last-16 clash with Dynamo Kiev after beating Young Boys 3-1 on Thursday to complete a 7-2 overall triumph.
Everton travel to the Emirates on Sunday to face an Arsenal side who could be short on confidence after being drubbed 3-1 by AS Monaco in the Champions League on Wednesday.
"Arsenal will not let the midweek game affect them," Martinez said. "We need to make sure we are fit and ready for an exciting game."
Everton will be without Tony Hibbert and Christian Atsu for the trip to third-placed Arsenal but Romelu Lukaku, who scored twice in the Europa League win on Thursday, will be fit despite coming off against Young Boys with a hamstring problem.
"Rom is fine," Martinez said. "Yesterday was about making sure he didn't accumulate too much work.
"His hamstring is fine and he has trained well this morning and I don't expect there to be a problem at the weekend."
(Reporting by Michael Hann, editing by Ed Osmond)
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