Barry joined Everton from Premier League rivals City on transfer deadline day.
"My last appearance for England was before the Euros," Barry told The Guardian.
"I made the squad on the back of winning the title and then picked up the injury.
"That was the downturn and affected my call-ups from there. Last season I still felt I was playing consistently well in a top team to merit call-ups but it's about opinions and other players can affect it too. But right to the end of last season I felt I was playing well enough.
"I spoke to Roy after the last Euros when he wanted to see how my injury was, but then you don't make the squad and you lose touch. I'm fine with that. I don't need explanations every time I'm not playing or in a squad."