Top scorer Cristiano Ronaldo had already offered his support for Ancelotti on Saturday, the Portugal forward saying he hoped to work with him again next season.
President Florentino Perez decided, however, that "a new impetus" was needed and fired Ancelotti two years into a three-year contract.
The decision, taken just a year after Ancelotti guided Real to their historic 10th European Cup triumph, prompted several important figures in the dressing room to show their appreciation for the coach on Twitter.
"Thanks for everything boss," Real's Brazil left back Marcelo wrote. "You are really great."
Germany midfielder Toni Kroos added: "Thank you boss. It was a pleasure to work with you. I wish you all the best for the future."
Colombian international James Rodriguez also thanked Ancelotti, saying he had "learned a great deal in a short time" from the 55-year-old, while France forward Karim Benzema expressed his gratitude for "two great years".
Perez, who has worked his way through nine coaches in two six-year stints at the helm of the world's richest club by income, said he did not mind the players advertising their affection for Ancelotti.
Going so obviously against the wishes of a majority of the squad may, however, make the job of whoever succeeds Ancelotti that much harder.
While Real's two captains, Iker Casillas and Sergio Ramos, have yet to comment in public following Ancelotti's dismissal, the decision of some players to make their feelings known on social media is unusual at a club that obsessively controls the flow of information.
Perez said the club would unveil Real's new coach next week, with local media reporting Napoli's Spanish manager Rafa Benitez as the front runner.
"The players have shown their affection for Ancelotti, the same affection myself and the supporters have for him," Perez told reporters.
"Not only does that not upset me but I think it is a natural response to have when someone is leaving Madrid after spending a period of time here," added the construction magnate. "It is gesture of fondness and affection from the players."
Ancelotti has said he plans to take a year out and will have surgery in Canada to correct a neck condition that was causing tingling in his hands.
(Reporting by Iain Rogers; Editing by Ian Chadband/John O'Brien)
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