The 32-year old midfielder joined the Toffees on a season-long loan on deadline day and his decision to head to Goodison Park caught the likes of Joe Hart and James Milner off guard according to England international Baines.
"I've known Gareth through the England set-up and I've always rated him really highly," he told the club's official website.
"The City lads on the last international break were saying that they can't believe that they haven't kept him and he doesn't play for them.
"That says enough about his worth for any team he plays in."
In regard to Barry's debut in Saturday's 1-0 win over Chelsea, Baines added: "Everyone rates him who he plays with and he has come in and shown what a great asset he is going to be for us.
"We've seen straight away what he can give to the team.
"I'm sure Gareth will tell you that he has not played as much as he would have liked and he has already produced a performance like that.
"If he plays like that most weeks, he is going to add to the team."