The on-loan Barcelona forward scored the opening goal of the 4-0 win on his first Barclays Premier League start and was a threat throughout the game.
Further goals were added from Seamus Coleman, Bryan Oviedo and Romelu Lukaku but there was only one person to talk about after the game.
"Gerard Deulofeu made a big impact and allowed the performance to create a scoreline which suggests it was easier than it probably was," said Martinez.
"I think he was really disappointed with last week. From my point of view I told him I thought he was outstanding against Liverpool (a memorable 3-3 draw) but he had two good chances and he felt he should have taken them.
"During the week he was left with a negative feeling that he didn't deserve, that is why I felt it was right for him to start and flush that feeling away and he was desperate to do that.
"I thought his first goal was sensational, I thought it was the moment of the game.
"The way he works for the team, the way he understands his role in the team has been very impressive.
"I am really pleased with the overall performance, that he was able to play 90 minutes and create so many chances and scoring the first goal was a pivotal moment.
"He is one of the most talented footballers in Spanish football, he is quite a unique talent, and the moment he made his Barcelona debut against Real Madrid in the Bernabeu aged 16 is when he caught my attention.
"There was a long list trying to take Gerard on loan and the fact he wanted to come to Everton was a fantastic feeling, and you can see why we worked so hard to attract him to the club."
The youngster tormented Stoke in the first half and Potters boss Mark Hughes, who gave a league debut to Deulofeu's former Barcelona B team-mate Marc Muniesa, admitted he was one of those who had tried to sign him in the summer.
"We were aware of him, we knew he was a talent and he is obviously a talent," said Hughes.
"We made an enquiry ourselves but unfortunately he came here and not to Stoke.
"He is a very talented boy and I am sure it will only be a loan deal, I am sure Barcelona will keep hold of that asset."
Hughes was less complimentary about his own side, however.
"We were poor on the day but credit to Everton, I thought they were very good and made it difficult for us," he added.
"The disappointing thing for us was up to 45 seconds prior to the half-time whistle we were very much in the game at 0-0.
"To concede right on the whistle, which is a key time in any game, is disappointing and lo and behold in the second half we came out and conceded early.
"That really shaped the game in a negative way. We tried to get back into the game but that just compounded our problems as we were a little bit over-exposed because we were trying to get back into the game.
"Four-nil was a little bit harsh on us. If we'd got to half-time at 0-0 I don't think the result would have been different but it might not have been as harsh."
Another of Everton's on-loan players Lukaku scored his eighth league goal of the season, but Martinez brushed aside criticism from Jose Mourinho at parent club Chelsea over the player's intentions for wanting to leave Stamford Bridge.
"The parent club are entitled to say what they like about the relationship with the player as he is their player," added the Spaniard.
"What is important is Chelsea wanted Romelu to get some playing time and allow him to develop and that is happening.
"The relationship is working extremely well, the player is scoring goals and working hard and is a true ambassador for Chelsea."
Lukaku reportedly said he would be prepared to stay at Goodison Park permanently if they qualified for the Champions League.
"I think that puts pressure on himself, that means he needs to score between 25 and 30 goals so it is fantastic he thinks that way," said Martinez.
Source: PA
Source: PA