A week after Amorim said his reeling team could face the threat of relegation, Lisandro Martinez and Amad Diallo scored United's first goals in the cauldron of Anfield since 2018, going toe-to-toe with the league's best team in a well-deserved draw.
"Today I'm allowed to be the only guy upset with the team," Amorim told reporters. "But today we were a team.
"I want to see my team play so much better, but I think the most important thing to address today is the mentality. That is the key for everything. Today, we were a different team, not because of the system, not because of the technical aspect of the game, the tactical aspect of the game.
"We faced the competition in the way that we are supposed to face every day, training and match. It doesn't matter the place... we need to face every day like that."
The draw saw United climb a spot to 13th in the table, still 11 points behind sixth-placed Manchester City and 13 behind fourth-placed Chelsea, but it felt like a win for the delighted travelling United fans who had braved the wintery drive.
United captain Bruno Fernandes, one of their best players on the day, was left frustrated by the game.
"I'm pretty upset," he said. "If we show this level at Liverpool, first in the league, why can't we do this everywhere?"
Amorim agreed.
"It's really clear," he said. "We lost three games in a row at home, some of the games we suffered two goals without doing nothing (defensively)."
Amorim had been optimistic that with no midweek games, he would finally be able to have a full week of training since his arrival in mid-November.
"I don't want to use that, but of course, when you train, you understand better the way we play, the positioning, the characteristics of the teammates, the things are really important. But I don't want to use that today," he said.
"Today is all about the focus when you are playing football, the focus on set pieces, the focus on passing the ball, not in the sloppy way, but in the way that we cannot lose one ball because in the other part of the pitch is (Mohamed) Salah, is (Luis) Diaz, so you don't lose the ball.
"If you lose the ball in some parts of the pitch, you know that we are going to suffer. If you have that mentality every day, you are a different team and I think that is really clear."
United nearly pulled off a victory with Harry Maguire missing a sitter with the last kick of the game.
"I don't think anyone would have predicted them scoring two goals today or nearly nicking it at the end. But the key is that they have to back it up," former United captain Roy Keane said on the Sky Sports broadcast.
"The argument to all of this though is that you can't just pick and choose when you want to turn up for a game at Manchester United."
