The Scot was confirmed as successor to Manchester United boss Sir Alex Ferguson, officially starting his job on July 1, after announcing he would leave the club at the end of the season.
England international Jagielka thanked Moyes for the service he had given the club and stressed it was important not to let it go to waste.
"Like the rest of the squad I have nothing but the highest regard for David Moyes," he told evertonfc.com.
"He is a first-class operator on and off the training ground and on behalf of the players I would like to place on record my thanks for the work he has done improving the team.
"It (his departure) was as much of a shock to the dressing room as I'm sure it was to Everton and our fans.
"All the lads wish him the very best for the future but we still have two important Premier League games to play and all our attentions will be focused on winning against West Ham and at Chelsea.
"Once the season is over we can collectively look forward in order to ensure we continue to build on the positive work of the past few seasons."
After much speculation earlier in the day Everton were first to go public with the news Moyes would not be staying beyond the end of his contract, which has six weeks left to run.
"Everton can confirm that David Moyes will leave the club at the end of the season," said a statement.
"The manager met chairman Bill Kenwright early yesterday evening (Wednesday May 8) and confirmed his desire to join Manchester United.
"The chairman, on behalf of the club, would like to place on record his thanks to David for the massive contribution he has made to Everton since his arrival in March 2002. He has been an outstanding manager.
"During his tenure at Goodison Park, David has taken charge of the team on over 500 occasions including four European campaigns.
"His final two games as Everton manager will be the remaining Premier League matches against West Ham United and Chelsea.
"Everton officials will start the search for a replacement manager immediately."
Moyes stressed his determination to go out on a high after 11 years at Goodison Park.
"I have had a terrific job at Everton, with a tremendous chairman and board of directors and a great set of players," he said.
"Between now and the end of the season, I will do everything in my power to make sure we finish as high as possible in the table.
"Everton's fantastic fans have played a big part in making my years at Goodison so enjoyable and I thank them wholeheartedly for the support they have given me and the players.
"Everton will be close to me for the rest of my life."