Having taken a two-goal lead after just 11 minutes through Sergio Ramos and Gareth Bale, the European champions missed a host of chances before falling apart defensively.
Ancelotti apologised to the club's supporters after the loss, angry at what he saw as a complacent performance.
"This is a loss that I do not like at all because I think occasionally you can play badly but, when you lead 2-0, you have to show the required attitude to see out the game," he told reporters after the match.
"It is my responsibility. Something has to change and it will. I am sorry because I do not like it that the team have played in this way. You have to quickly change the things that have not gone well."
The defeat means that Madrid already trail Barcelona by three points in and champions Atletico by one in the early standings in La Liga.
Ancelotti feels that it is a difficult match to review after his side started so impressively but rejects claims that his team's poor performance was down to the departure of Xabi Alonso to Bayern Munich.
"It is not easy to assess this match because there were two parts to it," the Italian remarked. "The first 30 minutes were very good and we showed great concentration. For the rest of the time it was very bad – we thought the game was over. We gave away too many fouls and corners.
"We didn't have an adequate defensive system in place. We were too soft at the start. The game changed a lot after that and we defended badly. We were lacking balance above all.
"This isn't a problem with just one player or another but a general problem. The team lost after a fantastic first half-hour. When there isn't a good attitude, it makes no difference if Xabi Alonso is there or not."
Ancelotti defended the performances of new faces James Rodriguez and Toni Kroos, adding that the result would not change the club's transfer plans with just one day to go until the closure of the summer window.
He continued: "The new signings still need time but they are adapting well. With a game like that it is always more difficult for the new players than it is for the others.
"This defeat changes nothing on transfers. We need to change our attitude and concentration in these types of games."