The Blues went ahead early on through a disputed Frank Lampard penalty, only to fall 2-1 behind when Ashley Young replied from the spot and then Emile Heskey headed in for Villa.
Chelsea left it late to turn it around as Didier Drogba fired in six minutes from time and then in the last minute John Terry slotted in for what looked like the winner, only for Clark to head home unmarked in stoppage time.
The result leaves Ancelotti's side fifth in the division and six points behind Manchester United and Manchester City, with United having a game in hand on Chelsea and City having played a game more than the Stamford Bridge outfit.
However, Ancelotti added: "Firstly, United have to win their game in hand. Obviously we must beat them when we play at Stamford Bridge and maybe then we can have a bigger say."
The Italian conceded Villa were the better team before the break but said he was delighted with Chelsea's response in the second half.
He stated: "I think that we had a fantastic reaction second half. We played very well, with a lot of energy, with a good spirit and when we thought that the game was won, we lost two points at the last situation.
"For this reason, I'm disappointed because at this moment, when we needed to win, it was our fault because I think we were not able to maintain concentration until the end.
"I'm disappointed because we worked very hard in the second half to come back into the game when 2-1 down. We did a fantastic job, we came back and scored to make it 3-2 and everyone thought the game was finished but a mistake with the last ball of the game cost us."
Ancelotti denied his players had paid the price for over-celebrating and added: "I think that it was not an over-celebration. It was a good reaction after the goal.
Houllier pleased to see Villa 'stop the rot'
"The last goal, yes, it was a mistake, because we conceded an easy cross and we didn't mark in the box."
Aston Villa manager Gerard Houllier, who was under tremendous pressure going into the game because his side had lost five of their previous six league matches, was full of praise for his players.
"We showed character, we showed bravery, we didn't bottle it, we played," he said. "At 2-1, we knew that Chelsea would throw everything at us to equalise and, in fairness, they did.
"I would have been extremely disappointed if we didn't get anything from this game but because I thought that, in fairness, the players had done enough to at least get a draw."
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