Holders Real scraped into the quarter-finals with a 5-4 aggregate victory but, having lost top spot in La Liga following defeat at Athletic Bilbao last weekend, their poor form continued against Roberto Di Matteo's men.
Real were forced to withstand a late barrage after former striker Klaas-Jan Huntelaar secured Schalke's win on the night with a fine 85th-minute strike at the Santiago Bernabeu.
Ancelotti's side have now lost four times in all competitions since the turn of the year - a marked contrast to the team that embarked on a club-record 22-match winning streak before the mid-season break.
Coach Ancelotti is aware of the pressure he is under, but has vowed to end Real's slump.
"I do not think about [being sacked]," he said. "I keep doing my work, trying to do it better. I need to do better.
"We must say it clear, we are playing very badly. It is pretty hard to understand, after what we did up to December. "
Real's latest defeat was met with a chorus of jeers from the Bernabeu crowd.
Ancelotti expressed sympathy with the home supporters, but maintained his confidence that his under-performing team will bounce back.
"The whistles from fans are totally deserved. This is going to motivate us more, for the next game," he added.
"We suffered a lot until the final minute, right until the end. The game did not go as we wanted. Anything could have happened.
"We have had problems, in all aspects of the game, attack and defence, fight, concentration, motivation. It was pretty clear.
"It is not easy to explain, above all we have lost some confidence in our play, in our identity, above all that.
"I have full confidence in these players, in all of them. The key to fix this problem is the players themselves, the coach too."
