Barkley opened the scoring against Manchester City on Saturday with a sensational curling effort from long range.
Although the visitors to Goodison Park turned things around to claim a 3-2 success, the performance of Barkley represented a positive for Everton.
The 20-year-old has enhanced his reputation significantly this season and is a strong contender to make England's squad for the FIFA World Cup.
"I've said it many, many times - he is a phenomenal talent. It think he is the best English talent that I've seen and worked with," said Martinez.
"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."
