The Spain Under-21 international came off the bench at the Emirates Stadium on Sunday and scored a superb equaliser to earn Everton a 1-1 draw against Premier League leaders Arsenal.
Deulofeu has made 13 appearances for the Toffees in all competitions so far this season and after needing a couple of months to settle into English football, he is now showing exactly why he is so highly rated.
After seeing Everton hold the Gunners, Martinez revealed the 19-year-old is in line to remain at Goodison Park for 2014/15 unless Barca decide they want him back.
"He has surprised me and everyone that he is ready now and wants to help the team," Martinez said.
"We have an agreement that the loan could be extended an extra year as long as the parent club do not need the player."
Everton have now gone eight games unbeaten since losing at Manchester City in early October, and that remains their only league defeat of the campaign thus far.
Having been impressed with their display in north London, Martinez added: "We showed we have gotten over that mental block in going away to those teams who are going to be challenging for the title and are being ourselves, which is a massive step towards where we are trying to get."
Midfielder Ross Barkley was at the heart of all Everton's positive play.
Martinez has urged England to be patient with the 20-year-old World Cup hopeful, who has earned three full international caps.
"Ross has incredible potential, we need to give him time and accept he is not ready yet, that he will take time, but he has absolutely everything to mark a real era in our (English) football," he said.