After fighting back from 2-0 down to draw 2-2 at Blundell Park, United were eliminated on penalties on Wednesday night by the League One team.
Afterwards, Grimsby goalkeeper Christy Pym said: “It’s not sunk in yet. I’m a Man Utd fan, so I’m half-fuming a little bit. Night’s like this is what you play football for. Just brilliant."
Bryan Mbeumo's penalty hit Pym's crossbar to hand Grimsby victory after an 18-minute shootout.
Pym also said: “I should have done a little bit better (in the shootout), shouldn’t I? I made one save to keep us in it and the boys have done the rest. It’s brilliant.”
Goalscorer Charles Vernam also said: “It was a nervy wait. When it just kept going on and on, you just never know. We scored and thought ‘right we have a chance’ and then they kept scoring.
“It’s an amazing feeling, one that will live with us forever. The message all week has been about belief and knowing how good we are and the gaffer’s instilled that.
“He (David Artell, manager) told us not to just turn up, there’s always a chance if we play the right way with the right intensity. Why can’t it be us?
“So to pull that off is an amazing feeling and we’re going to enjoy the moment.”