The 20-year-old midfielder has been tipped to join Baines in the England squad for this summer's World Cup following a string of impressive performances this season.
Despite Barkley's meteoric rise, Baines believes that the youngster should not have too much expectation heaped on him.
"I didn't have the same sort of trajectory as what Ross has had," the full-back told Sky Sports News. "Mine was a steady growth really and didn't miss out too many steps on the ladder.
"Ross has burst onto the scene and the spotlight was thrust upon him straight away. He is a top player and a top talent for the country.
"We sometimes have a tendency to do that with young players. I think that it is important that we sometimes give them a bit of time and leeway to develop."
Everton return to action on Saturday when they welcome Swansea City to Goodison Park in the Premier League.