Martinez fully supported the decision to postpone the Palace match and believes handling the fixture congestion will show the club is a challenger for a Champions League place.
"Once you get the game called off then you need to adapt to it," he told The Liverpool Echo. "Looking at the squad I think we are capable of coping with a big amount of fixtures.
"If you want to have the mentality of a big team you have to be able to cope with a lot of games from the period of February until the end of the season."
Everton sits sixth in the league table with 13 games remaining, with the team five points behind Tottenham in fifth and eight off Liverpool in the final Champions League place, though the Toffees now hold a game in hand over each.
As well a top-four Premier League finish to aim for, Everton remains in the hunt for the FA Cup, and faces Swansea City in the fifth round on Sunday.