Everton were beaten 2-1 by Manchester United in the FA Cup semi-final at the weekend.
Martinez opted to pick Aaron Lennon ahead of Deulofeu at Wembley, with the young Spanish winger only being utilised as a late substitute.
When Deulofeu did enter the field he completely changed the game, giving Everton a new outlet going forward.
And Wright said: “You see Deulofeu… he came on and literally changed the game. That’s the stage for him. I’m watching the game, and I’d start him. I’d find somewhere for him to play. It’s the stage - that’s what he wants to do.
“Some of the decisions his made will come back to haunt him.”
Deulofeu set up Everton’s equaliser during the contest, with his vicious cross being diverted into his own goal by United defender Chris Smalling.
The former Barcelona man also created a great chance for Romelu Lukaku soon after, but the powerful forward was unable to convert.
That miss proved costly, as the Red Devils went on to triumph in the tie 2-1, with Anthony Martial scoring a late winner.
Martinez is now under serious pressure, and his omission of Deulofeu is not the only team selection decision to receive criticism.
Tim Cahill also took to Twitter to criticise Martinez for not using Kevin Mirallas until late on after the match.
Van Gaal brings on Herrera for the assist and still has more on the bench. We bring on Deulofeu and he produces and MIRALLAS might of helped— TIM CAHILL (@Tim_Cahill) April 23, 2016