What the same way which broke Barca's dominance by beating the points total in the league? Ramos is the one sounding like a **** then surely if that's the case.
They only did so momentarily, and Barcelona matched that feat this season. And there lies the problem, in my opinion. Madrid lost the title race early on, which was bound to have consequences. Players, fans and suits alike could tolerate Mourinho's style both on and off the pitch while they were winning, but once results stopped going their way cracks started to show.
The board, for the most part, stood by him, going as far as to sack Valdano for a perceived lack of cooperation with José.
The bigger names, aside from the portuguese players (Mourinho's relationship with them was, for the most part, very good), started having minor differences with him and his staff for various reasons (it is claimed that Ramos had an argument with Mou and Casillas leaked this to the press) and this began expanding to the rest of the squad. Once it was clear for everyone to see that Mourinho was leaving, even the ever-loyal Pepe, who had seen his place usurped by Varane, turned against his manager. A few players, however, stood by him (Higuaín, Di María, Essien, Coentrao, Cristiano, Özil...) till the end.
His relationship with the press had always been rocky at best, due to the nature of the spanish press (pro-Barcelona vs pro-Madrid) and it worsened as Mourinho's relationship with media-darling Casillas became strained, alienating even Marca, arguably Spain's top "pro-Madrid" newspaper.
Regarding the fans, you'll find mixed reactions. On the one hand, his three titles with the club and a few successes against arch-rivals Barcelona make many consider his tenure as a coach as a success. However, for a large chunk of the local fanbase, an apparent lack of "Spanish-ness" in the squad, coupled with perceived mistreatment of fan favourites like Casillas, disagreements with Toril (RM Castilla's manager), lack of opportunities for youth players (nothing new here, they complain about this season after season, coach after coach), displeasure with the style of play, ungentlemanly behaviour by both José and his players (lack of "señorío"), among others, were the main complaints of the supporters. The lack of trophies this season, coupled with an ever-futile quest for "La Décima" and the first defeat in over a decade against Atlético de Madrid (at the Bernabéu and in a cup final!) were the final nails in the coffin.
The problem is much more complex than it looks. For madridistas, winning is the most important thing, but how you do it is important as well, and this isn't limited to the style of play. And if you're not doing the things "the Real Madrid way" and you're not winning, either, you'll be in deep ****, whether you're José Mourinho or the king of Spain himself.