The 32-year-old joined the Toffees on a season-long loan during the last few hours of deadline day in search of first-team football.
"I haven't been pushed out at all," the Manchester Evening News quotes Barry as saying. "I've trained every day with the first team, so there was nothing like that, but when the squads were announced, I wasn't travelling for friendlies, and so the writing's on the wall when that happens.
"If you want to be playing regular first-team football, then it's time to move. I just don't think I'd have been a happy person, sitting there not playing. Once the Premier League started and I was sitting at home, knowing I wasn't involved, I wasn't a happy person."