Some senior figures at the club criticised the manager's lack of a plan B, sources said, after a performance in which Madrid dominated possession at the Bernabeu but were unable to muster a single shot on target.
Madrid tend to rely on Vinicius Junior to open up opposition defences, but the winger was kept at bay by defender Ronald Araujo, as the home side were unable to find other ways to break down Barca's defensive line.
Sources said Ancelotti's decision to pick both Toni Kroos, 33, and Luka Modric, 37, in the Madrid starting lineup had also been questioned, for what was expected to be a physically demanding encounter.
Kroos and Modric have been in inconsistent form this season and there is now an internal debate at the club over whether Madrid can afford to pick both from the start, with Aurelien Tchouameni, Eduardo Camavinga, Federico Valverde and Dani Ceballos available as younger alternatives.
The displays of fullbacks Dani Carvajal and Nacho in Thursday's game have also been questioned. Sources said more was expected of Carvajal in attack, while Nacho -- playing at left-back in the absence of Ferland Mendy and David Alaba -- was unable to get forward in support of Vinicius.
A source close to the dressing room told ESPN that a number of players should take a look at their own recent performances in what has been a demanding, unusual season, punctuated by the World Cup in Qatar.
However, with two Clasicos coming up -- in LaLiga on March 19, with the Copa del Rey return leg on April 5 -- the squad are determined to turn the situation around, pointing to the example of last season, when Madrid overcame early doubts to win a Champions League and LaLiga double.
Sources close to Ancelotti say that he is focused on Madrid and intends to see out his contract, which runs until June 2024.
"I'll stay as long as the club wants," Ancelotti told ESPN before last week's Madrid derby. "I love Madrid, the food, the football and the city."