Real have found themselves under fire after losing two of their opening three Primera Division matches as well as being defeated by Atletico Madrid in the Spanish Supercopa on the eve of the new season.
Long-serving club captain Iker Casillas, meanwhile, found himself jeered by Real fans during last weekend's 2-1 home league loss to Atletico, a result that left the European champions trailing six points behind leaders Barcelona in La Liga.
However, Real went some way to appeasing their supporters with a 5-1 Champions League mauling of Basle at the Bernabeu on Tuesday, and Ancelotti believes there is nothing to panic about as his side prepare to face promoted Deportivo La Coruna on Saturday.
When asked about the gap to Barca, Ancelotti said: "We're not thinking about that, we're thinking that we have to improve physically and tactically.
"We did well against Basle and it's not the time to worry about that. We have to have the necessary calm because the season is long. One thing I'm sure of is that Real Madrid will fight to the end in all competitions.
"I don't understand the concern.
"Everybody should have faith in this team. We won the European Cup four months ago and we could win it again."
Madrid have won on two of their last three visits to La Coruna, but prior to that they went 18 years without tasting victory at the Riazor, and current Depor boss Victor Fernandez is hoping to cause more problems for their star-studded visitors.
He said: "I want us to go out to win. If we go out to draw we will lose. We're not going to be suicidal, but we'll be different to the Eibar match (Depor won 1-0)."