Amorim conceded his future was on the line after Sunday's derby defeat at Manchester City. However, he insisted he wouldn't change his playing system.
Speaking on Sky Sports, Neville said: "I'm worried about the manager, I'm worried about what's going to happen in this next few weeks
"I don't think it's a time for panic, but I've seen this before, we've seen this film."
Neville added: "We can't be getting into October where Man Utd are 14th or 15th in the league otherwise the manager will be in trouble.
"They have to start winning quickly.
"Next week if they lose (to Chelsea), they would go to 15th and 16th.
"And that's where they can't be, having spent £200million and giving him a pre-season.
"It's five games in and before you know it you're in October and they're in the bottom half of the table.
"There's got to be a turnaround pretty quickly, and the manager's idea has got to land very quickly with the players."