The end of the Scot's 11-year tenure at Goodison Park was confirmed when he was announced as Manchester United manager as successor to Sir Alex Ferguson. Moyes, whose contract expires in six weeks, will remain in place for Everton's final two matches of the season before he officially takes over at Old Trafford on July 1.
Kenwright's job now is to find the right man to not only maintain his manager's good work but also take the club forward. "He's a great manager and Manchester United are very lucky," said Kenwright.
The Toffees chairman stressed there would be no instant decision - unlike when he recruited Moyes from Preston in 2002 - and they would be scouring far and wide for the best candidate.
He added: "We've had a good 11-year adventure with David and it is my job and the club's job to get a worthy successor and build on what David has brought to the club and hopefully move on from there. We will be out there finding the right man for this football club.
"It is important from here on in Everton continues in the David Moyes tradition, in the Everton Football Club tradition, with an equally significant manager - because he has been a significant manager for 11 years.
"Eleven years ago I made a decision and it was an instant decision when I met David, but I don't think that can happen this time. We have to be very seriously out there looking to see what kind of candidate is out there who can take the club forward.
"I won't lie to you and say there is no-one in my head, no-one in Everton's head or Everton supporters' heads.
"Everton fans are no fools. They took to David Moyes instantly. I'll be looking to those supporters to get the kind of guidance that true football fans can give to a chairman.
"It's important they get the right man. Of course it is important the club get the right man but they know the adventure they've had for 11 years and they want it to continue and continue to grow and that is vital for them. It's a very important part of my life to see that they are not let down because I don't want them let down."
Meanwhile Roberto Martinez has no intention of allowing speculation over a summer move to Everton to get in the way of his side's first FA Cup final.
Wigan head to Wembley anchored in the Premier League relegation zone knowing their manager is hot favourite to replace David Moyes at Goodison Park following the confirmation he will join Manchester United on July 1. Wigan chairman Dave Whelan has already insisted the Toffees are not a big enough club to attract someone of Martinez's calibre.
However, whilst he allowed himself a chuckle at Whelan's intervention, it is clearly not a debate Martinez is prepared to get into, either with the media or, more importantly, Everton - at least not now. "It would be a waste of time for anyone at the moment," said Martinez.
"The chairman has a fantastic knowledge about the game and you can ask him anything. He will never turn away from an answer. But the most important thing for me is to be ready for Saturday.
"Whatever people say doesn't affect us. This is the peak of our season and we are not going to lose any focus or concentration. All that matters is Wigan Athletic. We need to fight to make our fans proud."
It is a shame for Wigan that the build-up to the biggest day in their entire history should be overshadowed by discussion of Martinez's future.
Yet it is part of the club's DNA to operate in the shadows given the enormous status of the clubs who surround them.
On one side, Merseyside, whose other mighty club had discussions with Martinez about filling their managerial vacancy last summer.
On the other, a club whose departing manager has made front and back page headlines in every corner of the globe over the past 24 hours, and another in Roberto Mancini, who will stand at the opposite end of Wembley on Saturday.
"We all know Manchester City are the major favourites and rightly so," said Martinez. "But there are many examples of major upsets in the past. It can happen but we will have to be perfect."
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