Club president Florentino Perez confirmed what local media had been saying for days on Wednesday, when he ushered Pellegrini out of the door to make way for the imminent arrival of Jose Mourinho from Inter Milan.
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"I came here with high hopes and great pride to manage this team. Unfortunately I wasn't able to do what I wanted to do and I had differences from the beginning of the season," Pellegrini said in a Cadena Ser radio interview on Thursday.
"There were a lot of disagreements in the club. I asked for them to keep (Wesley) Sneijder and (Arjen) Robben, who were two very important players for me. I missed having a debate on sporting issues, with the coach included.
"As (former Real coach and current Spain boss) Vicente Del Bosque said, even the club show no respect for the position of the coach, and they don't give them the authority internally or externally.
"Florentino's project is extraordinary but I think he's got it wrong."
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Pellegrini was signed from Villareal last June to take charge of a team that had 250 million euros spent on new players such as Cristiano Ronaldo, Kaka and Karim Benzema. Robben and Sneijder were sold to help offset the costs.
Under Pellegrini, however, the team fell at the first hurdle in the King's Cup, were knocked out of the Champions League at the last 16 stage, and finished second behind Barcelona in the La Liga.
Not going farther in Europe was Pellegrini's biggest frustration, he said, along with: "Not having felt more involved with the project."
The Chilean added: "I haven't spoken to him (Perez) since August. I respect his stance of the president. He has a sporting project in which I don't fit."
Even before the end of the season, local media were talking up the possibility of Mourinho coming in as his replacement for next season, even though Pellegrini had another year left to run on his contract.
"It hurt... above all because they had already tied up a new coach which isn't ethical," Pellegrini said, before criticising Mourinho for talking to the media about wanting the Real job.
"I wouldn't have spoken about a team that already had a coach in place. It isn't very ethical, but he is a coach that has proven he is a winner in every team he has been with."
