The hosts ultimately prevailed at Anfield as an incredible set of spot-kicks ended in a 14-13 scoreline after a 2-2 draw through 120 minutes on Tuesday.
Albert Adomah ended up the villain, following in the footsteps of Patrick Bamford and Raheem Sterling by failing to convert.
Mignolet said, unsurprisingly, he had not encountered anything similar in his career.
He told Sky Sports: "No, not that long. I have obviously done a few in pre-season and I think the lads have practised them really well.
"You always want to progress. We have done that and that is the main thing. We wanted to finish it earlier but we got the result we wanted and that's all that mattered."
The initial game was similarly dramatic, with Bamford netting from the spot in injury time of extra time.
That forced the penalties after Suso's first goal for the club had put Liverpool back ahead following Adam Reach's leveller for Middlesbrough.
Such was the nature of the drama that it was almost forgotten young debutant Jordan Rossiter had made an immediate impression with a 10th-minute goal.
"I couldn't have dreamed of that. I can't even remember what I did when I scored. I just went mad a bit," Rossiter said.
"I am still young and looking to build on that performance. Hopefully I can do that in the future."