The Blues boss branded the display the worst of his reign after John Obi Mikel's error cost a late equaliser.
Ancelotti raged: "It was the worst display since I came here. In the second half we lost intensity, lost concentration, we played too slowly and too soft.
"For this, I'm not happy. We have to play 90 minutes with intensity and concentration. It's not important about the result. It's important to play our best every game and I told the players that.
"We had the possibility to close the game but we didn't play well. It was right that APOEL drew the game.
"I see every day the players training very well and I think that it's only a psychological thing for this evening."
The Italian is also sweating on a hamstring injury to Michael Essien that rules him out of Saturday's Everton clash.
The only Chelsea star to escape Ancelotti's fury was 18-year-old Gael Kakuta.
He added: "Kakuta is the only good thing for tonight. He showed his talent and I think he will be the future of Chelsea."
STAR MAN
To surrender the lead once is bad enough. To do it three times in a week is unforgivable.
Going out of the Carling Cup on penalties at Blackburn was one they could shrug off. But defeat in the Premier League at Manchester City suggested that Chelsea might not be quite as good as they think they are.
Those suspicions were confirmed last night as they were denied victory yet again by a late APOEL equaliser.
In the grand scheme of things, the loss of two points is no real handicap to Chelsea's European ambitions. They still finished top of Group D and remain unbeaten at Stamford Bridge in their last 30 games.
Yet Carlo Ancelotti fears a disturbing complacency has crept into his team's play since they crushed Arsenal at the Emirates at the end of last month. And the Italian knows he must get to grips with the malaise - before it finishes him off.
The Chelsea boss does not need reminding Phil Scolari was given the boot after a not dissimilar run of results earlier this year. And a £6.5million-a-year contract will be no insurance against the elbow if things do not improve dramatically.
Qualification for the knockout stages of the Champions League is the bare minimum for Ancelotti. But Roman Abramovich is not paying top dollar just to get through to the last 16.
He expects the biggest trophy in European football - and he is not a man who tolerates failure. It was Ancelotti's success in lifting the Champions League twice with AC Milan which landed him the highest-paid manager's job in the world. But he can forget those lofty ambitions if this week's dismal efforts are anything to go by.
And now the real hard work starts as Chelsea prepare for next week's second-round draw in Switzerland. Any illusions that Ancelotti might have harboured about the strength of his squad were shattered as they struggled and failed to see off the Cypriot champions.
Never in his worst nightmares would he have imagined any team of his being put through the wringer by APOEL Nicosia. Yet those fears were realised after just six minutes last night when skipper John Terry was unable to deal with a low cross before Marcin Zewlakow fired past keeper Ross Turnbull.
For Turnbull, making his first start for Chelsea, it was a dismal way to begin his Stamford Bridge career even though he was not to blame. It was the first goal Chelsea had conceded at home in 968 minutes of action since Stephen Hunt netted for Hull on the opening day of the season
The noisy Cypriot fans had something to sing about three minutes from the end when Jon Obi Mikel sold Terry short with a sloppy pass and sub Nenad Mirosavljevic struck.
Seven goals conceded in the space of seven days by a team which prides itself on its rock-solid defence. Not good enough Carlo. Must do better Chelsea.
Ross Turnbull 6
Juliano Belletti 5
John Terry 6
Ricardo Carvalho 6
Yuri Zhirkov 6 - Booked
Jon Obi Mikel 5
Joe Cole 7
Michael Essien 7
Florent Malouda 8 - STAR MAN
Didier Drogba 7
Gael Kakuta 7
SUBS:
Frank Lampard (for Essien) 6
Fabio Borini (for Kakuta) 5
Subs not used: Hilario, Ivanovic, Bruma, Philliskirk, Anelka.
well, the last was a game, Chelsea did not have to lose, and they are certainly not at full strength.. all a smoke screen..