The 20-year-old England midfielder is set to make his continental debut for Everton on Thursday when they take on Lille at the Stade Pierre Mauroy in the Europa League.
Barkley has already experienced plenty of things in his short career, and on the prospect of giving him a run-out in Thursday's game, Martinez said: "I think the bigger the challenge for Ross, the bigger the response.
"It was such a joy to see his big smile getting on the plane. He has missed two important Europa League games and I know he has found it difficult."
Barkley made his first appearance of the season on Saturday having recovered from a knee injury, and his return to action has given everyone at Goodison Park a lift according to the boss.
Ross Barkley was part of the England World Cup squad in Brazil
"To see him back on Saturday was a real positive for us,” he said. "In the Premier League, you have a unique level of pace and power but in other leagues you get a bit more of a tactical game where strategy is important. Getting all those experiences is good for any young player."
Having overcome the challenge of his rehabilitation from injury, his next one on the continent is exactly the type that the youngster needs to continue progression, added Martinez.
"I think one of the benefits of getting into the Europa League was for the young players to get that European experience.
"It is important for them to face different teams that pose new tactical problems. Straight away it develops your understanding and awareness.
"It is a phenomenal competition for young players. It is exactly what they need."
Thursday’s match is the first of a double-header between Everton and Lille, with the reverse fixture following on 6 November. The Blues top Group H with four points while the French side are third with two after two rounds of games.
