The Latics beat Manchester City to record a historic victory on the penultimate weekend of the campaign last May but then were relegated from the Premier League three days later with defeat in a rearranged match at Arsenal.
This season the FA Cup final has been moved back to its traditional place after the last week of the Premier League season and Martinez believes that is the correct decision, even if it came too late to help the Latics.
"The final got in the way of the final week," said the Spaniard, who is looking to win the trophy in back-to-back years with his Everton side facing Swansea at home in the fifth round on Sunday.
"Obviously you shouldn't rely on going into the final week to achieve your aim in the league.
"For any club going into the final week of the season, whatever your aim is in the league, you shouldn't get punished for playing in the FA Cup final, it should be the opposite - it should be a moment to treasure and enjoy.
"I don't think it was a really helpful issue when you had to play the FA Cup final the weekend before the final games of the season, which meant we had to play three games in the final week.
"I think that (making the final the last match of the season) is the right thing for every club involved in both competitions."
Wednesday's postponement of their league match with Crystal Palace because of high winds around Goodison Park throws up the potential for fixture congestion further down the line if the Toffees continue their cup progress.
Martinez, however, does not necessarily see that as a negative.
"While you are progressing through the fifth, sixth rounds and semi-final you build momentum and expands the squad because youngsters get an opportunity to show that they can do," he said of his experience with Wigan.
"It makes you stronger as a squad as you progress. Success in the cup can really help in the league and the other way around.
"It is just finding enough strength in the squad to face both competitions if you are going to get a fixture pile-up."
After Swansea, Everton travel to current league leaders Chelsea the following weekend but Martinez refuses to see the next fortnight as season-defining for his sixth-placed side.
"The longer you get involved in a cup competition is always a defining moment because every round you are fighting to stay in the competition," he said.
"Staying in the competition further than the fifth round is always significant but there is nothing different because we want to finish the season as strong as we can.
"It is not just doing well over the next two weeks, that is not good enough for our standards.
"The work we have done in the last eight months has got this squad ready with an incredible competition for places.
"Now we are starting to get every player back and we are in the best moment of the season to face the final third.
"The season will not be decided on the success of the next two weeks."