Apoel's first-ever home game in the group stages of Europe's most prestigious competition was threatening to fall flat as the Premier League side dominated the first half and deservedly led at the interval.
Juliano Belletti created the opening with a neat dribble before feeding Anelka, who finished with his customary clinical coolness.
The second half was a different story, however, as the hosts had enough sights of goal to justify earning a point from the encounter.
Savvas Poursaetides profited from an error by Florent Malouda and his shot deflected off John Terry before being kept out by Petr Cech.
Constantinos Charalambides had mustered an effort in the first period and he really should have scored and sent the home fans wild when steering a late header just off target.
Chelsea did have other chances themselves, most notably when Malouda latched onto a Frank Lampard cross but could only fire against Dionisis Chiotis's legs, but this was a far-from-vintage display by the West Londoners, who were still without suspended star striker Didier Drogba.
At least Joe Cole came off the bench again to promote his claims for a place against Liverpool in Sunday's big Premier League fixture but Ancelotti knows his side must improve if they are to collect three points at the weekend.
"It was a good result but perhaps not a good performance," said the Italian afterwards. "We started with good control, scored a goal and we had opportunities to do quick counter-attacks after that, but we didn't do this.
"In the second half, it was different. We tried to control the game with possession but we made a lot of mistakes.
"Nicosia played very well in the second half and deserved to draw this game. This is football.
"I'm not satisfied. I wanted Chelsea to play better and to take more control, to play with courage. But I think that, in this moment of the season, it's normal. We have to change, for sure.
"We have to play better. In the first half, the team showed good application of the system and of their defensive duties.
"We took good control in defensive positions, but the second half was totally different. We lost a lot of balls. We allowed Nicosia to get back into the game.
"I'm not angry with the players. I have a lot of faith in this team and these players. I was a player for a lot of years myself, and I know when things don't go well.
"I'm not afraid, not angry with the players.
"The only thing is that I'd like Chelsea to play better than we did."
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