The 29-year-old emerged as a rising talent at the Toffees for whom he made 131 appearances under the Spaniard.
Barkley's playmaking abilities caught the attention of Chelsea in 2018, although his career at the Blues failed to live up to the hype.
Now at Nice in Ligue 1 and set to be a free agent in the summer, questions are raised over the future of the midfielder's career.
However, Martinez has revealed his delight for Barkley moving overseas and claims that he's a star whose play has been restricted.
Speaking exclusively to talkSPORT, he said; "I'm really proud that he's decided to go abroad. I think Ross is one of those players that at times he hasn't been understood.
"As a British player, he's not a player that fits in a system, and I think that's been a big problem for him. I think if Barkley would have been born in Spain or in a different culture, they would appreciate more his incredible physicality for a technical player.
"Normally in football you've got real exceptional technical players or exceptional physical players, Ross had both. But he wasn't a player that fitted in a specific role and he wasn't a player that would do the work for the system.
"That's a shame because when we saw Ross in our first season at Everton, you could see what he had.
"Right and left foot, the way that he scored so many goals from distance from both legs, the way that he would go past players at pace, that individual dribbling quality that he had.
Most read in Football
Messi move confirmed, Postecoglou to Spurs, Mourinho confronts ref, Mount to Man United
Celtic preparing for Ange Postecoglou to leave for Tottenham job
Mourinho tells Taylor he's a 'f****** disgrace' after waiting in car park to confront ref
Mason Mount agrees personal terms with Man United as they prepare offer for Chelsea star
"It's a shame that he's one of the players that's always been asked to do something that he couldn't, being restricted and being part of a system and doing things at an average level."
Martinez was arguably the first manager to allow Barkley to unleash his talent as he scored 21 goals and assisted a further 17 during their time together at Everton.
He provided 23 goal contributions in 100 appearances at Chelsea, but has had a limited impact at Nice.
Barkley looks set to leave the French side in the summer, with his potential next club yet to emerge.