Mbeumo had earlier got Manchester United back in the match, scoring in the 75th minute before English international Harry Maguire netted the equaliser just before fulltime.
Grimsby Town defender Tyrell Warren scored his side’s second goal which gave them a 2-0 lead at the break, his first goal for the club.
“Amazing. Surreal really. I’m lost for words,” he said after the win.
“I personally think I should score more. What a great time to score,” he added.
Midfielder Kieran Green told the host broadcaster that the advice from their manager ahead of the shootout was all the pressure was on the Premier League side.
“It’s unbelievable. I think it’ll be one that’ll live in the history of this club for a long time,” Green told ITV.
“I know a lot of the fans were looking forward to it, we were looking forward to it, so it’s one that will stick around forever, I can imagine.
“I think that we went 2-0 up and everyone was probably surprised to be in that situation. I know they’ve come back from 2-2 and it’s two-all, let’s have it right, we’d have taken 2-2 at the death, so 2-2, them getting the equaliser at the end, we’re still the team winning at that point and we’d take that going into the end.
“Going into the penalty shoot-out, the gaffer said to us, ‘lads, all the pressure is on them’, and it was really.”
More to come...