Man United hosted Man City for the final Manchester derby of the season on Sunday with neither side able to capitalise on the other’s poor form.
Amorim, who replaced Erik ten Hag last Novemeber, has failed to turn the club’s fortunes around as they look set to complete the worst Premier League season in their history.
Sitting down in 13th with just 38 points from their 31 games, Keane, 53, was left questioning Amorim’s methods.
Keane said on Sky Sports: "The manager is going to stick with it. That's the gamble he's taking. If he's not getting football results we're talking about next year when he will no doubt get an opportunity to get players in the summer, we will be able to judge him better.
“That's his belief and philosophy and that's fine. But I like the philosophy of winning football matches. I don't remember sitting with the players I played with - and some brilliant managers - when we discussed our philosophy.
“United tried to play out from the back and got caught a couple of times. I don't like that. I'd like to be proven wrong and United are in the top four or five next season but I don't see it. I saw Forest the other night, I was kicking my cups of tea over. They were never going to score."