Real beat Swiss side Servette 2-0 in Geneva on Sept. 8, 1955 and claimed the first of five straight titles by beating Stade de Reims 4-3 in the final in Paris the following June.
The tournament was an initiative of French sports daily L'Equipe and its then-editor Gabriel Hanot. World governing body FIFA gave their backing under the condition it was organised by their European counterpart UEFA.
"I must confess that we had no idea how significant the tournament would become," Spaniard Gento was quoted as saying in an interview with Spanish sports daily As on Tuesday.
"We went to play and that was it," added the 81-year-old former left winger, who is the only player to win the competition six times.
"Nobody explained to us what would happen, neither the competition format nor that it was going to be something important for many years to come.
"I don't think we really realised what it all meant until we won the first title in the final in Paris.
"Then we were able to see what the European Cup was all about. It was something indescribable."
Real, the world's richest club by income, have amassed 10 continental crowns, their latest coming in 2014 when they beat city rivals Atletico Madrid in the final in Lisbon.
Gento said he would "give anything" to see footage of the match in Geneva but as far as he was aware none existed.
"There was no television, no videos," he said.
"I would love to be able to show my grandchildren those images from 60 years ago.
"Now that we see everything, I miss being able to have more of my things from that era."
Real have been drawn in Group A of the latest edition, which was renamed the Champions League in 1992, along with Paris St Germain, Shakhtar Donetsk and Malmo.
They begin their bid for an 11th European crown at home to Shakhtar on Sept. 15.
(Writing by Iain Rogers, editing by Amlan Chakraborty)
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