The Red Devils endured a bumpy ride on their way to the final but injury-time goals from Teddy Sheringham and Ole Gunnar Solskjaer overturned Bayern Munich in incredible fashion to seal an historic treble.
Cole says an inspirational half-time team talk from Sir Alex Ferguson played a big role in inspiring his side's comeback at Camp Nou.
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"The manager was still been very positive at half-time, even though we were a goal down and not playing particularly well, which helped.
"He then said to us 'this is the European Cup final - some of you may never get here again - make sure when you come in at full-time that you have given your all and left nothing on the pitch'. That is what he is all about.
"It's a great feeling to actually lift that trophy, to know that you've achieved something you've wanted to do since being a kid.
"It took a hell of a long time to sink in, a hell of a long time. I always say we've won it with two of the scruffiest goals in European Cup history but it was meant to be."
Check out the video above for the full interview with the former United and England striker.