Perez said on Monday that the Spanish giants "have to be united" as they look to claim trophies both in football and basketball.
Perez's comments come amid a turbulent time on the football front, with Madrid having been knocked out of the Champions League semi-finals last week and on the verge of surrendering their Primera Division title to arch rivals Barcelona.
Madrid coach Jose Mourinho, who looks set to leave the club this summer, was also booed by home fans prior to Saturday's Primera Division win over Real Valladolid, while he came under fire from centre-back Pepe after the game for his comments about Iker Casillas.
Pepe said Mourinho needed to show Casillas more respect after his fellow Portuguese appeared to slight Madrid's long-serving goalkeeper with his comments about Diego Lopez on Friday, saying he wished he had bought the stopper sooner.
Madrid can still finish the season on a high, though, with a Copa del Rey final against Atletico Madrid to look forward to this month, while the club's basketball side are also chasing honours in the Euroleague, and Perez wants everyone to be pulling together.
He said: "Soon we will have two new challenges, the basketball Final four and the Copa del Rey final.
"We have to be united, give it everything and do our best for our supporters. Our players will do it."