The ex-Toffees boss Moyes has come under pressure recently, with the Red Devils currently sitting in eighth place in the Premier League.
Jagielka reckons the Scot has had to deal with numerous selection dilemmas and has struggled to find his ideal starting XI.
"It's difficult because it was always going to be the hardest job in the world to go there," he told The Independent.
"He has a young squad and who do you pick? He has probably got 25 (first-team players) and most of them have a value of at least £10m-plus.
"That was always going to be the hard part, to find his squad and find his feet.
"The fixture list was horrific for him. That puts extra pressure in the games that you expect Man Utd to win and they have come unstuck at times."
The former Sheffield United centre-back, expected to feature in next year's World Cup for England, believes that Moyes will be confident in his own ability and will lead United back to the summit of the table.
He said: "He's a great manager and as much as Man Utd won the league everyone expects it is easy to take them to the next level, it is a little bit of a rebuilding session.
"I am sure they will stick with him and if they do so he will be in the job for a long, long time.
"Once things do start clicking, they'll be flying back up the league."