The former Aston Villa midfielder netted the goal which secured a 3-2 aggregate win for the Foxes, sparking wild scenes at the King Power Stadium.
It capped a remarkable turnaround for last season's Premier League champions, who have looked rejuvenated of late following Claudio Ranieri's sacking.
And Albrighton hailed the support of the Leicester fans on one of the biggest nights of the club's entire history.
"It’s tremendous, everything about it. We had the belief from minute one that we could get a result and we have done that," he told reporters.
"To walk off that pitch knowing you’re through to the last eight of the Champions League is something else.
"It is very difficult to remain calm, but with the fans behind you and knowing the prize at the end it does get you through.
"Coming here, you see the fans around the ground as we arrive. All the flags and displays, walking out to that was brilliant.
"Through the game the fans were fantastic and after the game was something I’ve not experienced before, even probably when we won the league. That was special but this was a different place."
Though Albrighton proved to be the matchwinner, he was quick the praise the performance of goalkeeper Kasper Schmeichel.
The Dane saved penalties in both legs of the tie as well as making a series of other saves, and Albrighton hailed the recent displays of the Leicester No.1.
"I think Kasper is the one who won us the tie, I would say. The two penalty saves were massive.
"Especially the one tonight, came at a crucial time. We took a lot of heart, a lot of relief and a lot of confidence going into those last ten minutes."