The Spaniard handed a second consecutive start to the 19-year-old for the visit of West Bromwich Albion and said that he has been "very impressed" so far.
Martinez claimed that Barkley is intelligent enough to fit into a number of different roles for the club, describing him as "an incredible talent".
"I've been very impressed with Ross. I think at his age it's incredible the manner that he has developed his game," Martinez told reporters.
"Sometimes you see a youngster with enormous potential and enormous talent and somehow you need to use that. With Ross it's the opposite.
"He can fit in in different roles, he's a thinker, he makes fantastic decisions in where the space is. I've been very impressed so far and I know he's going to go from strength to strength, he's an incredible talent."
Barkley had spells on loan at Sheffield Wednesday and Leeds United last season.