After Chelsea's shock exit on Tuesday night, United were beaten 3-1 on spot-kicks by Middlesbrough last night at Old Trafford after Ashley Young missed the decisive spot-kick.
Boro will now host Everton in the last-eight after the quarter-final draw was made after last night's matches.
After wins over Aston Villa and Bournemouth respectively, Southampton and Liverpool will go head-to-head at St Mary's.
Reds boss Jurgen Klopp was pleased to have registered his first win at Anfield.
Also last night, Man City thrashed Crystal Palace 5-1 to set-up a quarter-final against Hull and the other last-eight tie will see Sheffield Wednesday visit Stoke.
