The Toffees struggled in the first half at Goodison Park after Aiden McGeady hit a post and trailed to Leandro Bacuna's 34th-minute opener.
Martinez said: "From our point of view it's the most satisfactory victory of the season.
"You could see in the first half we were very cagey and wary and that stopped us getting on the ball and having the fluency that we normally have.
"When you hit the post and then you concede a goal, it becomes a real test of character, and I thought the way we reacted in the second half was one of the most pleasing aspects that you can have as a manager.
"With the character and the talent and the desire in that dressing room, I couldn't be prouder. It's a moment to get really excited about the end of the season after that sort of performance."