Carlo Ancelotti's side surrendered first place in the Premier League as two pieces of sloppy defending from set-pieces condemned the Blues to a 2-1 loss.
Frank Lampard failed to get a proper connection when he tried to head a corner clear and Villa's Richard Dunne escaped Ricardo Carvalho's attentions to score with a diving header.
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It got even worse as Petr Cech couldn't collect another corner and Didier Drogba allowed Villa defender James Collins to run free and head the winner.
Those two blunders took the number of goals Chelsea have conceded from set-pieces to six already this season and Germany midfielder Ballack admitted Chelsea's squad held a no-holds-barred discussion to avoid any repeat in Wednesday's Champions League tie against Atletico Madrid.
"We have no problem to criticise each other in the dressing room. A good team and strong players have to do this," Ballack said. "We have done this. After that we shake hands and go back on the training pitch.
"The way we lost was very disappointing. We watched the video of the match and everyone could see who made the mistakes.
"That is football, somebody has to make the mistakes. We trained on set-piece situations but it is all about individual mistakes.
"We have to work on it. It was just one game but it was obvious that we lost on set-pieces. We have to be aware.
"Everyone has to improve their movement and defensive organisation. It is a point of personal attitude. Don't concede a goal.
"It happens once now and hopefully it won't happen again. We have to focus on our strengths, which is playing good football and winning games."
Although Ballack missed the Villa defeat with an ankle injury, he joined captain John Terry in underlining that the individual mistakes must stop.
"His (Terry) reaction on the pitch shows he takes a big responsibility. Not just for himself but for the team. That is what you need, you need the players to see it can't happen again," Ballack added.
"I think I have to do this as well, not just because of my age. I have a few years behind me and I have been through a few situations.
"I have to speak to help the team, but not just me, everyone has to take responsibility.
"Of course the weaker teams in the league, they try to score against us from set-pieces because most of the time we will have more possession on the ball."
Blues boss Ancelotti spent part of Monday's training session working specifically on defending set-pieces, but he believes no amount of pre-match preparation can completely eradicate mistakes by individuals in the heat of a big game.
"Yes, we worked on this particular situation. It is important to work on this. It is important to pay attention to set plays during the match," he said.
"But it is difficult to train set pieces, it is like training a penalty kick. It is different.
"We work because we have to improve. You can do a good match like against Aston Villa but if you don't pay attention for six seconds you can get a bad result and this is not good."