The Santiago Bernabeu outfit broke a 32-wait for the European Cup by beating Juventus in Amsterdam thanks to a second-half strike by Predrag Mijatovic.
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"Each year, we had psychosis for the title," he told AS.
"We had a great team, a great atmosphere and experienced players. We were given the opportunity of our lives and we couldn't miss it.
"I have never experienced a celebration like it. La Septima changed the history of our club. Madridismo won in the stands. It was incredible."
Hierro went on to win the Champions League two more times in his career, beating Valencia in 2000 and Bayer Leverkusen in 2002.
Madrid will look to claim their 10th European Cup - La Decima - against arch rivals Atletico on Saturday in Lisbon.