United started the game going in front after 10 minutes, Bruno Fernandes putting the Red Devils ahead but Diogo Jota equalised 11 minutes before the break with Roberto Firmino putting the Merseyside outfit ahead on the brink of half time.
Liverpool's number nine put the game out of sight two minutes after half time getting on the scoresheet once again. United did threaten to get back into the game deep into second half as Marcus Rashford scored from a tight angle but Mohamed Salah put any doubt at rest, his goal in the 90th minute sealed all three points for the away side.
United came into the game on the back of a good 3-1 victory against Aston Villa at Villa Park on Sunday evening. The Red Devils came out the traps quick after Allison's poor pass out of the box was pounced by Edinson Cavani, the Uruguayan firing wide. The United striker picked up possession on the edge of the area but dragged his shot wide of the post, as Allison's mistake went unpunished.
Fernandes fired United into the lead after some poor marking from the Reds defence. The Portugal international wrapped the outside of his right foot around the ball, his strike taking a huge deflection before going in.
Eric Bailly had allegedly brought down Nat Phillips inside the box in the 27th minute, with referee Anthony Taylor ruling out the penalty after going to the VAR monitor. Taylor changed his original decision and claimed that Bailly got a touch before Phillips went to the ground.
Replays showed he made the correct call the second time around. Jota made things all square as the Reds scored from the resulting corner as he backheeled the ball, beating Dean Henderson on the third occasion.
Roberto Firmino was the man to head Liverpool into the lead, the goal coming at the perfect moment before half time, he grabbed his second of the night as the Reds punished United for some sloppy defending, the ball spilt straight into Firmino's path as the striker tapped home and gave Liverpool a two goal cushion.
Jota could have made it another goal as he rattled the upright from close range, as that could have been the game right there for Liverpool. United did grab a goal back as Rashford took Cavani's pass into his stride before rolling the ball past Allison and into the bottom corner. But it was Salah who had the last laugh as he raced away to score Liverpool's fourth of the night, curling the ball past Henderson.
After the 4-2 loss, the United boss spoke to the media and was disappointed with the final result.
"They deserved the win. We conceded goals in key moments of the game. We didn't build on the momentum or break up their momentum. We gave them atleast two goals really. Then we scored again, had a massive chance, key moments against us."
On Liverpool's attacking style of football at Old Trafford which caused the Red Devils several problems. But Solskjaer knows his team started the game with the right intentions:
"Their shape and their pressing is very aggressive. We created our own downfall. The second goal you probably expect no foul there then it's a bad moment to concede just before half-time. The third goal we gave them and that's really poor. The attitude was right and the focus was fine, we were ready for it. We didn't build on the good times. We should have gone more for it at the start of the game. Sometimes we let them off the hook and let them play out."
He knows Harry Maguire has a very important role to play within the club although he wasn't available today:
"Everyone would miss their captain and leader. Harry has been amazing since he came to this club. We will miss a player of that quality but we have players that are ready to step in. Harry Maguire has been really important for us so of course we're going to miss him but he's out so we have to deal with that. It's about regrouping and building our own confidence again as we have two games and a final."