Fulham's goalkeeper, Bernd Leno, emerged as the shoot-out hero, saving penalties from Victor Lindelof and Joshua Zirkzee, while the visitors converted all four of their attempts.
The home crowd expressed their frustration, booing the team off at halftime, as United found themselves languishing in 14th place in the Premier League, reflecting their ongoing struggles this season. United, who have claimed the FA Cup a record 13 times, reached the final in the last two seasons and lifted the trophy by defeating Manchester City last year.
However, this defeat means there will be no journey to Wembley for them this time, leaving the Europa League as their only remaining chance for silverware. The atmosphere around Old Trafford has been tense, with recent announcements of 200 job cuts and disappointing performances, including a draw against Everton and an inadequate win over lowly Ipswich.