Despite the Red Devils going on to win 2-1, he revealed he had feared a loss to a 10-man Chelsea would have added even more pressure on Amorim.
"Do you know what? I thought even with 11 men, I thought they started the game really well and caused Chelsea problems,” he said on The Wayne Rooney Show on BBC Sport.
"And then when Chelsea went to 10 men, I was worried! I was thinking, it's just like United now to go and lose the game.
"And then I think that would have brought a whole lot of more pressure on the manager. But I thought they played really well first half and then second half, it's silly, it's naive from Casemiro.
"As soon as he got his yellow card, I was watching it in the BBC studios with Danny Murphy and I said that I'd take him off. He's going to get sent off. You just knew what was going to happen and it could have cost us in the end."
Manchester United will look to extend their winning streak when they face Brentford in the Premier League on Saturday.