The Barcelona loanee was in irrepressible form throughout the game at Goodison Park, as he marked his first Premier League start by opening the scoring in the 4-0 rout by finishing off a finely crafted team move on the stroke of half-time.
Deulofeu then played a key role in goals two and three from Seamus Coleman and Bryan Oviedo as Martinez's side overwhelmed Stoke with an irresistible attacking performance, Romelu Lukaku adding the fourth.
The 19-year-old impressed after coming on as a substitute in Everton's 3-3 draw with Liverpool last week, and Martinez insisted his menacing display on Saturday came as no surprise as he was determined to make amends for missing two opportunities against their local rivals.
"I think he was fairly disappointed with last week - from my point of view I thought he was outstanding when he came on against Liverpool but he had two very good chances and he thought he should have took them," the Everton manager said.
"I thought his goal was sensational. The way he works for the team and the way he understands his role in the side is very, very impressive."
Martinez made three changes to the team that drew with Liverpool last time out, with Deulofeu and Oviedo being joined in the starting XI by Leon Osman at the expense of Kevin Mirallas, the injured Leighton Baines and Ross Barkley.
And the former Wigan Athletic boss was delighted with the incoming trio, saying they were key in his side being able to play to the same level as the Merseyside derby.
"I was a little bit worried before the game if we'd be able to maintain the tempo and intensity we had in the previous game, (but) the way we controlled the game was very pleasing ... (the) players with fresh legs made a big impact," he added.
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