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 a historic treble.
Mario Basler had put the German side in front after six minutes and the game had remained that way for the next 85 before fate changed course, prompting a feeling that Cole admits took "a hell of a long time to sink in".
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"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, the season that got us to the final and the way we played and some of the goals we scored in that season ... when you score some scruffy ones like that, when you consider the run we had in that competition, sometimes things like that happen.
"It was meant to be."
Check out the video above for the full interview with the former United and England striker.