As soon as the legendary Sir Alex Ferguson announced on Wednesday that he is to step down as Manchester United boss at the end of the season, Moyes was installed as favourite to succeed his fellow Scot.
United have wasted little time in wrapping up the appointment of a man they hope can maintain the success they have enjoyed during a trophy-laden era under Ferguson, with Moyes set to join on a six-year contract this summer.
Kenwright, who took Moyes to Goodison Park from Preston North End in March 2002, is understandably disappointed to be losing a coach who has offered so much to his club over the past decade, and admits he faces a tough task in finding a suitable replacement.
He told Sky Sports News HD: "He's a great manager and Manchester United are very lucky. It will be tough for all Evertonians to say goodbye to him, he's a great manager. Let's be honest, we couldn't stand in his way because he is out of contract. He's out of contract and it was his decision. He's made it.
"We've had a really good 11-year adventure with David and it's my job, and the club's job, to get a worthy successor and build on what David has definitely brought to the football club and hopefully move on from there.
"It's been an extraordinary 24 hours, one that I wasn't prepared for. It's important now that we finish the season against West Ham and Chelsea, that we maintain our position and that from here on in, Everton Football Club continues in the David Moyes tradition, in the Everton Football Club tradition, with a significant manager.
"He has been a significant manager for 11 years and I know, I'm pretty convinced, that Evertonians will only look upon David Moyes with gratitude and admiration. We will be with him for the next two games and then we really will be out there finding the right man for this football club.
"It's an extraordinary football club and one that is worshipped by its fans. They are the people, more than anything, over the last 24 hours that I've been thinking of, that we've been thinking of.
"Eleven years ago, I made a decision and it was an instant decision. I don't think that can happen this time, you've got to be very seriously out there looking to see, and we will be, what kind of candidates are out there that can take the club forward."
Asked if he already has candidates in mind, Kenwright added: "No, really no. It's been a year now since David and I sat down and went through this season, next season. We've been planning for next season until very recently. David Moyes has always been my manager and I'd seriously hoped and thought that he would be the manager next season.
"I won't lie to you and say there is no-one in my head, there is no-one in Everton's head, there is no-one in Everton supporters' heads.
"Everton supporters are no fools, they took to David Moyes instantly. I will be looking to those supporters, not to get individual names, to get the guidance that true football fans can give to its chairman and its football club. You can't individually poll each of them, but it is important that they get the right man.
"Of course it's important that the football club gets the right man, but they know the adventure they have had for 11 years and they don't want that to stop. They want it to continue and continue to grow, that's vital for them. It's a very important time of my life, to see that they are not let down. I don't want to see Evertonians let down."