United were knocked out of the Europa League despite a spirited fightback as Liverpool completed the job to progress to the quarter-finals.
Anthony Martial's penalty gave Louis van Gaal's side hope of a memorable turnaround, but Philippe Coutinho's brilliant goal on the stroke of half-time put the tie to bed.
2-0 down from the Anfield leg, the Reds started brightly and, roared on by a raucous Old Trafford crowd, carved out three good chances inside the opening 20 minutes.
Jesse Lingard should have done better with a header, Martial also went close and Juan Mata skewed wide from six yards.
David de Gea was soon called into action at the other end, though, with a stunning save to keep out Coutinho's low goalbound effort.
United simply had to score first and were given the chance to do just that when Martial went down under a challenge from Nathaniel Clyne just beyond the half hour mark.
The Frenchman stroked in his twelfth of the season from the spot to give United a lifeline but the goal lifted Liverpool out of their shell and the visitors twice went close to a quickfire leveller.
Daniel Sturridge struck the bar from a free-kick and Jordan Henderson spurned a glorious opening when one-on-one.
Marcos Rojo then somehow failed to convert from five yards and United were to rue that miss as Jurgen Klopp's side equalised right on half-time.
Coutinho had a lot of work to do down the left, but worked his way past Guillermo Varela and into the area before clipping in a wonderful dinked effort over De Gea on the angle.
Despite now needing four to progress, Van Gaal's side manfully continued to press as Marcus Rashford lashed a shot wide and Marouane Fellaini nodded straight at Mignolet when well placed.
With time ticking on and the tie slipping away from United, Liverpool looked the more likely to come away the winners on the night.
Sturridge hammered an effort wide on the counter attack, whilst the excellent Coutinho continued to cause United problems.
The Brazilian playmarker twice forced impressive stops from De Gea, Fellaini fired over and Jesse Lingard saw another penalty appeal turned down.
That proved to be the last action of a frustrating night for United as Klopp's side take their place in Friday's draw for the quarter-finals.
Overall team performance: 6/10
United Faithful Man of the match: Daley Blind