With the scores tied at 1-1, substitute Lingard gifted the Swiss side victory with a misguided backpass deep into stoppage time.
Solskjaer said after the game, Solskjaer said: "That happens in a game. That's football. Up and downs.
"You've got big moments, you've got moments that go for you and against you. He'll handle that one, and we'll handle it."
Maguire added: "With Jesse, no footballer likes making mistakes but it's obviously part and parcel of the game. We're humans, every footballer makes mistakes, we'll learn from it, he'll learn from it.
"He'll pick himself up and be ready to go on Sunday, that's part and parcel of football. But of course, discipline is a big part."