The competition has famously come to the Reds' rescue in the past, most notably in 1989/90 when Sir Alex Ferguson's side won it - his first trophy as United manager - after finishing 13th in the league.
More recently, Louis van Gaal and Erik ten Hag steered their sides to FA Cup glory, having posted final league positions of fifth and eighth respectively.
But Amorim dismissed the notion, put to him by ITV reporter Gabriel Clarke, that it was vital for United to find the club's fighting cup spirit at the death against Leicester City and remain on the road to Wembley.