A string of impressive performances over the past couple of seasons has seen Baines become one of the most highly-rated left-backs in Europe.
Meanwhile, Irish international Coleman enjoyed a return to form last season after being deployed in his more familiar right-back role.
When asked if there was a better pairing in the Premier League, Jagielka told EvertonTV: "I don't think so. I think Bainesy, rightfully so, has been taking all the plaudits, but quietly going about his business is Seamus.
"I am delighted for him. He's such a great lad off the pitch that he deserves all the success on it.
"Now, I think he is beginning to realise how much of a good player he is and how much of a good player we think he is - not only the players and the staff but the fans as well."
Everton defeated Juventus in the International Champions Cup in San Francisco.