However, the pressure on Moyes's shoulders has lifted slightly after guiding his side to the quarter-finals of the Champions League following victory over Olympiacos on Wednesday night.
"Transition is a big thing," West Ham's official Twitter page quotes Allardyce as saying. "When one of the greatest managers in the world leaves, transition is big.
"When someone else comes in, they have to be given time to make the changes they need to do."
The Hammers will take on United at Upton Park in the Premier League this weekend.