Moratti, who celebrated his 65th birthday when Inter won the Italian title last weekend, was overcome with emotion as they became European champions for the first time since 1965 when his father Angelo was president of the club.
"It's like a dream, a beautiful emotion. The team felt the responsibility and played a perfect match. It's great to feel the same sensation as so many years ago," he said after Saturday's compelling match at the Bernabeu Stadium.
"This is fruit of the work and dedication we have put in and the character we've shown on various occasions.
"We worked out what was needed, a bit of luck, a bit of everything. Winning the Champions League is about details," he told Italian TV.
Inter striker Goran Pandev, who worked tirelessly up front added: "I wouldn't have believed it, if you had told me at the start of the season.
"I had an ugly spell at Lazio. Now I've won three trophies.
"We know it will be hard to do it again but Inter have to try to win all the competitions we take part in."
BETTER TEAM
Moratti's delight after his club claimed a treble, having already won the Italian league and Cup double, was in stark contrast with Bayern's honorary president Franz Beckenbauer.
He said if the Munich side's suspended France midfielder Franck Ribery had played the outcome would have been different.
"We played with too much respect in the first half," he told German TV channel SAT 1. "If he had played he would have got everyone going.
"But Inter were the better team over the 90 minutes and they deserved it."
Bayern defender Philipp Lahm agreed.
"I think we played with too much fear in the first half. We weren't courageous enough. The second half was significantly better on our part.
"The hope was always there and we had that great chance just after halftime. Mistakes are punished in such a game."
Bayern goalkeeper Hans-Jorg Butt also said the better team won on the night.
"In the spirit of fairness, you have to say that Inter deserved to win.
"Right now disappointment is the overriding feeling.
"Inter defended very well. We couldn't get our game going and were unable to get past their defence.
"They have some great strikers up front. But it was a great achievement to get to the final with this (Bayern) team."
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