Barkley opened the scoring against Manchester City on Saturday with a sensational curling effort from long range, only for the visitors to turn things around to claim a 3-2 success.
|1/3||Ross Barkley is 1/3 with William Hill to make England's World Cup squad|
"I've said it many, many times - he is a phenomenal talent. I think he is the best English talent that I've seen and worked with," Martinez told reporters. "The character that goes along with those qualities is quite special.
"We need to give him good care and good support to fulfil his potential because he is going to be terrific news for Everton and for English football."
The manager has praised his Everton players for upholding the club's integrity during the loss, with rivals Liverpool ready to take advantage of any slip by City.
"I think everyone that watched the game understood straight away that if anyone questioned our integrity - not just as a football team but as a football club - they had not reason to do it," he said.
"The effort, the character of the players, the intention of winning the game was clear for everyone to see from the first second until the last.
"The way we celebrated Ross Barkley's goal is as big a roar as you got at Goodison for the whole season.
"So I'm proud of the football club that we were very much a team wanting to win. I think it's clear that we tried absolutely everything to beat this Man City side.
"In the last 20 minutes we gave a proper, proper go. We showed an incredible bravery in everything we tried to do from the first second to the last.
"We tried to win a football game and I think it's fair to say that we didn't deserve to lose the game."