Arbeloa replaced Xabi Alonso earlier this month as Real coach and enjoyed an impressive win against Villarreal on the weekend.
Garay told Marca: "A dressing room like Real Madrid's is very difficult. Big stars, and it's complicated to manage.
"I think the coach has to have a lot of character to be able to manage a dressing room like Real Madrid's and achieve important things."
Ex-Real midfielder Ruben de la Red insists he cannot see any difference between Arbeloa and Xabi.
Speaking at the same legends function, De la Red stated: "I don't think there's that much difference between what we had before and what we have now in terms of pressure and the style of play.
"Sometimes things don't go our way, and it's not the coach's fault, nor the striker's for not scoring. Now the team is doing well and eager to win everything they play for... just like before."