Liverpool manager Jurgen Klopp was left to rue a number of missed chances as his side's bid to win four trophies in his last season came to a dramatic end.
"After 2-1 up we had so many chances where we have to kill the game off and the rest is already history," Klopp told ITV.
"We are nearly there in normal time, nearly there in extra time and we lost the game. That’s all right, I cannot ask the boys for more.
"We’ve had a much more intense season so far, I think everyone knows that, we just have to count the games, and today it was hard because United have quality, took a lot of risks. I absolutely respect that.
"Congratulations to United for going to the semi-final. We have a game less, or two games less, who knows, and now we try to use that in the next few weeks."
Manchester United manager Erik ten Hag was delighted with his side’s start to the game and their resolve after Liverpool looked to have taken control.
"I think the first 30, 35 minutes was for me the best minutes of our season," Ten Hag said.
"We were really acting as a team but then gaps came up between the lines and you can’t allow this against Liverpool, they’re one of the best teams in Europe and then they outplay you.
"Also after half-time it continues and we had to change, we took risks, we went one against one and the players did wonderful.
"The mentality, the attitude was so great and they had a strong belief to win this game. They went for it and they got it."
Diallo, who admitted he had forgotten he had already been booked before taking off his shirt in celebrating his winner, told ITV: "I think we deserved this win.
"We played very good today, one of the best games of the season, so I am very happy for this win.
"Against Liverpool, it’s a very important moment, so I think it’s the best goal of my career.
"When he (Garnacho) gave me the ball I wanted to give it to him again but I think in this moment it was good for me to shoot.
"I forgot the first yellow so I’m really disappointed for the red card but the most important thing for me is to win."
The United players were all too aware they were playing to keep their trophy hopes alive for the season.
Captain Bruno Fernandes told ITV: "It was in our minds. We said our goal for the rest of the season is getting into the top four and trying to win the FA Cup.
"We’re going to do everything we can to get the two goals that we have, until the end of the season.
"The FA Cup is a big trophy for the club, (in) this country. We want to get into the final. We know it’s going to be tough, good teams in the semi-finals, but we’re going to do everything we can to get there."
