United came from behind to win 2-1, with Palace struggling in the end after playing in France on Thursday at Strasbourg in the Europa Conference League.
After Jean-Philippe Mateta had put Palace ahead, United stormed back after the break with goals from Josh Zirkzee and Mason Mount.
Amorim said afterwards: "It was small details that helped. The pace and intensity was better in the second half. I could see that Palace were getting tired at the end of the first half and knew they would suffer if we scored.
"We went on to control the game well away from our goal and in the opposition half. We controlled the game well but just have to be careful about what we did in the first half.
"It's the runs and you could see it with Joshua Zirkzee and how he connected with the team through the second ball. You have to explain that to the players but we have experience of being like that (tired) from last season when we played midweek."
On whether scoring will boost Joshua Zirkzee's confidence, he continued: "Scoring is important but it's not just the goals. They give confidence but Joshua has also improved a lot in how he holds the ball. That should give him a lot of confidence. He influences the game and that's important to our game. He needs to maintain that level in training.
"They have the quality and we have more players in the squad who can score. I'm really happy with them. Joshua (Zirkzee) hasn't had many minutes and Mason (Mount) works really hard."
On being in the top six, Amorim added: "In this moment I just want to evaluate our team. We need to evolve and create variety in how we build-up - that's the most important thing."