Barkley made his senior international debut with a substitute appearance in England's 4-0 win over Moldolva on Friday night.
The classy midfielder was rewarded for his fine early form for Everton this season with a maiden call-up to the England squad.
Jagielka is a big admirer of the 19-year-old and he was delighted to see him make the step up to the England side.
"He's quite a quiet lad and doesn't talk that much but on the pitch he just enjoys playing," Jagielka told the Liverpool Echo.
"But Ross just takes it in his stride and loves playing football. He gets on the training ground and does his thing.
"I don't think he realises how good he is half the time. It is so natural and refreshing to watch.
"He's really enjoyed being with the squad and that's what you love to see, especially with a young lad.
"He's had so much expectation chucked on his shoulders and had to deal with a couple of bad injuries.
"So as well as the plus points, there has been a lot of negativity in his career but he seems to have come through that really well.
"He is playing well for Everton and that is the reason he got called up and on Friday when he came on he gave us a little lift."