The Toffees found themselves frustrated after comfortably boasting more attempts and possession than their Welsh counterparts, but Garry Monk's side - without a shot on target - held out for a point.
It was not the 'openly-contested game' that Martinez expected, and the Spaniard - who managed the Swans for two years - says that it was "disappointing" to see them abandon their adventurous brand of football.
"It's like when you go to the cinema to see a fantastic movie then you get let down a little," he told Sky Sports News.
"I thought two teams who are technically really very good and the control of the ball is always very good. The philosophy of the game is really similar so I expected an open contested games.
"It was disappointing to see them trying to run the clock down and take the tempo out of it and try to hit us on the counter but everyone is allowed to play the way they want."
Monk's side moved up to sixth in the Premier League table following the result, while Everton sit ninth.