The Barcelona loan man opened the scoring after a lively first half and the result was sealed through strikes from Seamus Coleman, Bryan Oviedo and Romelu Lukaku later in the game.
Deulofeu provided two assists for his team-mates and Martinez did not shy away from singling out the Spanish international after a classy display.
He told reporters: "Gerard is one of the most talented young footballers in Spanish football, a unique talent. I was a big admirer of Gerard the moment he made his debut with Barcelona’s first team against Real Madrid at only 16.
"We were one of the clubs on a long list that wanted to take Gerard on loan and the player, with the backing of Barcelona, wanted to come to Everton and that was a fantastic feeling.”
Martinez did admit that Deulofeu has cut a frustrated figure with the lack of opportunities this earlier this season but refused to view that as a negative.
He added: "He wants to fight for his position and that is exactly what we need. It is not a frustration in an unhealthy way.
"It is about playing when you are ready and I always felt it would be January, February when we were going to see him ready to play. It has surprised me that it has been a lot earlier."
Stoke manager Mark Hughes admitted that he failed in an attempt to persuade Deulofeu to join him at Stoke."We knew he was a talent. We made an enquiry ourselves. Unfortunately he came here and not to Stoke. He’s a very talented boy."