The 20-year-old played 65 minutes after recovering from a knee injury on the eve of the campaign and was instrumental in the 3-0 victory against Aston Villa, pulling the strings as Phil Jagielka and Romelu Lukaku scored before Seamus Coleman, also coming back from injury, added the third.
Martinez admits he was not considering Barkley for selection until the youngster changed his mind in a training session on Thursday.
"The truth is eight days ago he was not an option in my mind to start the game," said the Spaniard.
"We benefited from the international break and he has been working individually and as a group and was phenomenal.
"On Thursday he put the ball in the top corner out of nothing and scored three goals in a little exercise we did and it was his way of telling everyone he was ready and he was desperate to be on the pitch.
"The way he trained I had no doubts and there was no risk from a medical point of view.
"The only doubt was how long he could last and he lasted longer than I expected and some of his movement off the ball early looked as if he had played every game this season.
"Sometimes you ask if he was born to play football
As human beings you are not born to kick a ball but he looks more natural with a ball than without it.
"He has a phenomenal knack to be born to play football
I thought he was sensational in that respect."
Everton began the day with the worst defensive record in the Barclays Premier League but only a second clean sheet of the season pleased Martinez as much as the display at the other end of the pitch.
"Sometimes when you look at performances where we didn't get the result we wanted or deserved you are looking at our defensive display as a team and it wasn't as solid or intense," he added.
"I thought today the difference was as a team we stopped Aston Villa carrying a threat and that is an incredible achievement.
"I thought we were very clever, very mature with what we did and defensively we looked very solid
(Goalkeeper) Tim Howard had little to do but when he had to he was phenomenal.
"To keep that clean sheet against the set-up of Aston Villa pleases me a lot."
Villa have now lost four successive league matches without scoring for the first time since January 2001.
"I don't think we deserved anything
I thought we started the game slow and that is not like us, normally we have come out of the traps quickly," Villa boss Paul Lambert said.
"Today was the first time I felt, with the run of games we've had, they hadn't justified themselves by playing the way they play.
"The goals were poor from our point of view
The first we have to stop the cross better, the second Brad (Guzan) thinks he should have saved it - that is coming from a guy that has saved us on many occasions - and the third goal is a ridiculous goal to lose.
"I don't think we did enough to win the game."
Source : PA
Source: PA