Cruyff, a three-time Ballon d'Or winner, passed away on Thursday at the age of 68 after losing a battle with lung cancer.
The Dutch icon achieved greatness as a player and successful coach.
"Johan has always been an idol for me," Van Basten told Voetbal International.
"I was always watching that great Ajax team's European games in the 1970s with players like Ruud Krol, Johan Neeskens, Sjaak Swart and of course Cruyff when I was young. They won three European Cups in a row, they were great to watch.
"Cruyff always drew my attention. That team was obviously very good, but Johan was a beautifully elegant player.
"I still remember meeting him for the first time. I must have been 15 or so. He was coming down the stairs and I was going up. I really felt an urge to shake his hand and to tell him to remember my name. But I never did. I think I had too much respect for him.
"Now that he's passed away, I realise how much he has done for football in general and also for Netherlands," concluded the Netherlands legend.