Aragones passed away on Saturday at the age of 75.
"I'm sure that he will be up there, dressed in red and white, feeling very happy with the courage the team showed. He himself was always a very courageous man with a lot of character," Simeone said of Aragones, who led Atletico to the 1977 Spanish title as well as three Copa del Reys during four different spells in charge of the club.
Simeone added: "When someone like Luis leaves us, you feel pain and sadness but I was really touched by the people today, and also how the crowd remained silent right up until the eighth minute, then chanted his name.
"It was wonderful that the minute's silence was observed in all of the stadiums through Spain."