Barkley made his debut in the 4-0 World Cup qualifying win over Moldova, while Jagielka played his part in both England matches - particularly impressing as the Three Lions gained a vital point in Ukraine.
"Ross is satisfied and excited - he never gets carried away," Martinez said.
"He is thrilled to have that opportunity. But he is a terrific listener and has got potential.
"Phil Jagielka has been at that level for a few seasons. He has massive influence now.
"He has been involved in four clean sheets in his last four games and he is at that stage where he is really enjoying it. He is at the peak of his career now."
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