The 88-year-old passed away on Monday after suffering a heart attack over the weekend in the Spanish capital.
The legendary former forward is widely regarded as one of the game's all-time greats and made his name during an 11-year spell at Real.
He played an integral role as the Madrid giants won the European Cup five years in a row from 1956 to 1960, and also won the Spanish title eight times.
After spending 12 years in search of La Decima - a 10th European triumph - they finally beat city rivals Atletico in Lisbon to pass the milestone in May.
And Perez spoke of his delight that Di Stefano had been able to witness the historic success.
He said: "These have been days of tears, but we felt the affection from around the world of football and sport in general.
"I am thrilled thousands of Madridistas have come to give him a final tribute.
"Alfredo Di Stefano forms part of our identity and the last match he saw was a reflection of the winning spirit that defined him and Real Madrid.
"He has been able to go with one more European Cup, thank you."
Di Stefano was named European footballer of the year in 1957 and 1959 and scored 308 times in 396 competitive appearances before leaving in 1964.