The Blues have now won just once in their last six league games and Ancelotti was clearly rattled by another sub-standard display from the Double winners.
"I am disappointed and angry,'' Ancelotti said. "Not just because of the result. We played good football in the first half and the second half was totally different. We played the long ball. We were a little bit scared. I didn't like this.
"We are working to play a particular kind of football and I don't understand why we have changed it. We have to look at it and I have to understand and change it. I don't think it is a problem of concentration. Everybody knew it was a very important game for us to move on from the difficult moment we are still in.
"We have to do better day-by-day on the training ground, in the training sessions. We have to work harder than we are doing. This is the way I know to move on in a difficult moment.
"The problem is on the pitch and we have to work to resolve this. First half the spirit was good. I saw the players in focus and concentrated with good tactical discipline. But in the second half they were scared, afraid and played the long ball.
"We needed to play better from the back and in the second half, it was the wrong way to play football. I am worried yes, because we haven't won a lot of games. The second half was totally wrong. We have to do better.''
Moyes accused Chelsea winger Florent Malouda of stamping on Neville but praised the response from his side following last week's 4-1 home drubbing by West Brom.
The Everton defender's decision to get up immediately from the altercation almost certainly saved the Chelsea winger from a potential red card.
"I have got to say Phil Neville did fantastic,'' Moyes said. "Malouda came in and stamped on him but Phil got up and ran away. But a minute later one of their players went and got him booked for nothing.
"It was disgusting. He helped keep Malouda on the pitch and a second later one of their players goes down easy and gets Neville booked. Ridiculous. But you need to have a look at Ivanovic's tackle in the 31st minute as well and look where the referee was.
"The second half we deserved the result. Chelsea had a few chances but then you expect that. It was tough for us in the first-half. The quality of our decisions in the final third probably cost us winning the game. But the players responded really well today. The players here tend to do that in the right fashion.''
"The goalkeeper could not get out of the way,'' added Moyes. "If it was me, I would want a penalty kick for it. But it definitely was not a sending off.''