Baines announced the end of his playing career following a 3-1 defeat to Bournemouth in July, having spent 12 seasons at Goodison Park, and is now a professional development coach with the club.
Speaking to shareholders, Kenwright stated: "One of the most important things of all to me in the close season… I didn't want Leighton to go. I wanted him to do another season.
"I tried but you just knew, he's a thinking, thinking boy. And a thinking left-back and a thinking footballer. And he didn't want to be remembered as anything other than a great left-back in Evertonians' eyes.
"He's a good lad, so it was great when we talked about a new role. And he's taken to it really, really well.
"He said to me at the end of the last game of the season - which wasn't good for Everton, against Bournemouth - he'd spoken to a couple of the young boys and said, 'You've really got to think about this…'.
"Not particularly first-team boys… I went, 'oh, that's impressive'. We spoke to Marcel and Denise."
He added: "You look at Ebbo (John Ebbrell), you look at Leighton…. And there's others you know, that we don't talk about in the background at Everton.
"Look at you, you're a Blue – where would we be without you! And I mean it, you've got to have the Blues there, I think, to really help the journey.
"I think it's important to Everton, more than probably some other clubs."