Jagielka, 31, is certain that his former boss will turn it around at Old Trafford.
And he believes Moyes' bosses should carry the can for his rough start as United boss.
Jagielka said: "I do feel sorry for him. The fixture list wasn't that kind initially. The transfers in the summer, the people who were making those decisions didn't help him out one bit.
"At Everton, where there isn't so much pressure, he could then grow into the season.
"He will roll his sleeves up and get the guys moving in the right direction and I am more than sure he will get United where they need to be.
"He just needs that little bit more time but sometimes, time seems a hard thing to get when you are at that top level.
"He has some good people around him and some great players in the squad. He just needs to add a few more players that he wants week in, week out.
"Once he gets that sorted and he gets more of his team, rather than a team he has been given, that is the acid test for him, once he gets the players in that he wants."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball