Carlo Ancelotti's men returned to the top of the Premier League table after a first-half double from Didier Drogba saw off their London rivals.
The Gunners had plenty of possession but could not turn it into goals.
Afterwards, Wenger congratulated Chelsea on their efficiency, while also taking a sly dig by claiming "we didn't get a demonstration of football".
But Germany captain Ballack maintains such determination to get the final result is what counts in the end.
The 33-year-old said: "We wanted to do our job.
"We knew the way Arsenal play. It is always the same style. If you play tactics like we did, you can beat them.
"This season and the season before they showed they weren't able to win the league.
"Wenger always says things like this when he loses to find an excuse.
"But football is not possession of the ball and playing a nice pass, football is about winning games and that is what Manchester United showed when they played them and what we did.
"We got the win because we were very effective and that was our strategy."
Ballack added: "Football is a mixture of winning games and good football physically, but also technically.
"We have a good mix in the team as we have shown this season and you can't do more. We are in first position and that counts."
The Gunners are now nine points adrift of the leaders, having lost successive matches against the top two following an impressive 10-match unbeaten run which briefly returned them to the summit.
Ballack said: "If you look now, it seems like a race between Manchester United and us — but four weeks ago, you could see how it was different and it can go quick when teams lose points."
Drogba once again proved too much for Arsenal to handle, as the Ivory Coast striker made it 12 goals in his last 12 games against Wenger's side.
He added: "In big games like this, he is there and that is why he is a big player.
"Didier has unbelievable physical strength, but he has great technique, is a great free-kick taker and has the nose of a striker.
"He has a lot of qualities and not a lot of players are like this."
Chelsea skipper John Terry led by example against Arsenal, his header from a corner setting up Drogba for the opening goal.
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The defender picked up a dead leg and will be assessed ahead of the trip to Everton on Wednesday night, while it has also been speculated Terry will be given a leave of absence from next weekend's FA Cup tie against Cardiff to deal with off-field issues.
Ballack maintains the team are united behind their captain.
The German said: "We can't do more than win games and that is what we have done.
"We are one team and we don't want to speak about the other thing, but the best answer we can give was on the pitch.
"We play for Chelsea and that is our job, which is why we have to win games and that is what we did.
"The team looked confident and settled.
"It is important to win, even in difficult situations — that is always the best answer."
Read more: http://www.thesun.co.uk/sol/homepage/sp ... z0ez1MQuJU
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