And the Toffees captain-elect, taking over the armband on a full-time basis next season with Phil Neville also leaving, thinks the new man's first phone call should be to Old Trafford to thank the newly-installed Manchester United boss.
Moyes got the perfect send-off on his final Goodison Park appearance in charge of Everton with a comfortable 2-0 victory over West Ham.
It was a performance the manager felt was worthy of a top-four team and while Everton are currently six points and several players short of that sort of recognition Jagielka insists they can approach the future with optimism.
"The guy has been here 11 years and has transformed the playing staff, the coaching staff, the facilities from top to bottom," said the centre-back.
"In the changing room we are obviously all gutted he will be leaving us next season but we understand the way football is.
"Frustrations must have been high. Teams around us that are potentially not doing as well but getting more finances made it a tough couple of years.
"To the same extent he has probably had the best squad he's had for a long time but he is still leaving that behind and we are still looking forward to next season."
The England international said it was impossible to assess just how big a void Moyes' departure would leave.
"That's a question I can't answer. Ask me in six months or a year's time and we'll find out," he added.
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