The ex-Old Trafford chief, 55, says the Special One needs time to allow the dust to settle from a turbulent few months.
Moyes also went on to say last weekend's last-gasp, comeback win over Newcastle was absolutely crucial.
The former Everton and West Ham boss said: "The big thing is that Jose has got himself a fantastic result at the weekend.
"It doesn't matter how you win but he did it in good style, beating Newcastle.
"I think that could settle things down a little bit. It takes time for all managers at Manchester United.
"Jose has been given time and I'm sure given more time – he's a winner and I'm sure he will go on to prove that."
Meanwhile, Moyes went on to add what the future may hold for him – saying he has offers from clubs across the globe.
The Scot boss said: "I have had offers to go to other parts of the world and manage in different places.
"I've had some offers back here as well.
"I'm waiting on the right one and going to try and choose the right one. We really enjoyed out time at West Ham last year.
"We had a great time, were really successful in where we took West Ham from to where we ended up.
"We will wait and see, I'm in no hurry."
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