Teddy Sheringham and Ole Gunnar Solskjaer pounced to deny Bayern Munich - and hand Fergie a unique Treble.
Striker Dwight Yorke scored 29 goals that season and played in that historic game.
He said: "The manager was in a buoyant mood before the game.
"We were in a great position having won the Premier League and FA Cup and there was a fantastic mood in the team, so he was totally relaxed. We just felt it was going to be something special. Roy Keane and Paul Scholes, two important people, were missing through suspension but the whole season had been a roller-coaster and we had coped with it.
"We had come back from being behind so many times, won games when we hadn't looked so great but always seemed to get through. Before the game the gaffer said to us 'This is a once-in-a-lifetime opportunity so lets go and create history. Let's not mess up'.
"But at half-time we were 1-0 down and just not playing well. The manager got us together in the dressing room and had a message that I've never forgotten. He said that if we didn't start playing we'd end up walking past that trophy at the end of the game and not be able to even touch it. But in the second half we were still huffing and puffing.
"I had a chance near the end to equalise. I'd scored 29 goals and with a few minutes left I had a great chance to score but didn't. But that team never gave in, that whole season was based on that mantra.
"The gaffer had made those sensational changes bringing on Teddy and Ole and they scored. When we equalised I still didn't see the next one coming - I was thinking about extra-time. Immediately after the game the gaffer was like a kid. The one thing that had eluded him for so long was the European Cup and now he finally had it.
"It was not just the manner in how we did it but what we had achieved that season, the history we had created by winning the Treble. The club had gone so far in the gaffer's time and this was the ultimate night. We had a big gala dinner after the game and after the chairman made his speech, the gaffer took the mic and said the season had just been incredible.
"But he told us to remember what had got us to this place - the togetherness, the hard work the determination and character. There is no other manager who will come close to what he has done. He taught me a lot about seizing the moment.
"That night we might have left it late but we seized the moment and thank goodness we didn't have to walk past that trophy without touching it."