Allardyce criticised the manner in which United cut ties with Moyes, and believes that time away from the game is the best thing for the former Everton boss, who spent 11 years at Goodison Park.
"I wouldn't advise him to come back into the game sooner," Allardyce told reporters. "I would come back later if I were him. He has done 15 years continuously - maybe even longer.
"To take some time with the family and reflect and enjoy life a little bit more without the pressures of particularly Premier League football will do him the world of good and then when he emerges again, he will come back a better manager than he already has been, and he has been one hell of a manager."
Moyes is reportedly being considered as a possible contender for the Tottenham Hotspur managerial job in the summer.