Joshua Zirkzee and Mason Mount struck in the second half to lift United above Palace to sixth in the table.
"It's important to win every game and again today was proof that if you play the same way but increase the way we fight for every ball and the small details, the certainty on the pass, the movements, we work on that in a different pace, we can beat anyone," Amorim said.
United's victory, only their second on the road in the last 12 games, came at one of the toughest places to play at Selhurst Park, where Palace had not lost in the league since February.
Although the hosts dominated the first half, Amorim, still under pressure after United's stumbling start to the season, was pleased with his team's intensity after the interval.
"We increased the rhythm in the second half. We took advantage of the opponent that we felt even in the first half, the last 15 minutes, (Palace) were tired," Amorim said.
"But the main change was the intensity and the pace of our of our game, even quality when we connect, especially with Josh in the second half, was different.
"So I think in the end, we deserved the three points, and I'm really happy to give that to the fans."
Zirkzee, who started in place of injured Matheus Cunha, scored his first league goal in almost a year and fourth since joining United in 2024.
"It is so important for a striker to score a goal," Amorim said. "He is not playing many minutes but the way he responds in the second half is really important. It's more important than just the goal.
"Again the small details — win one first ball for us to win the second ball. The connection is so important for our game. The goal is really important for our team and for him."