The Reds were beaten by Amad Diallo's goal in stoppage time of extra-time at Old Trafford on Sunday, with that strike earning the hosts a 4-3 win.
Jürgen Klopp's team led 3-2 at half-time of extra-time through a deflected hit from Harvey Elliott, before Marcus Rashford equalised in the 112th minute.
Earlier, Liverpool had recovered from Scott McTominay's opener to go 2-1 in front thanks to goals late in the first half by Alexis Mac Allister and Mohamed Salah.
United then forced extra-time with Antony's 87th-minute leveller and would ultimately edge a thrilling contest in dramatic fashion.
Due to rights restrictions, highlights for international subscribers will be available from 72 hours after the final whistle.
