The Gunners found themselves two goals behind inside 17 minutes as Juan Mata and Frank Lampard had the home side ahead at a snowy Stamford Bridge before Theo Walcott pulled one back in the second half.
It was the second defeat on the trot for Wenger's Arsenal and although he admitted being frustrated at some of the referee's decisions, his players were not exempt from copping some of the blame.
"We had a similar start to Man City last week, didn't defend too well and gave them too much incentive," he said.
"We didn't play well in the first half, but we were much more dangerous in the second half, with a different attitude.
"Unfortunately we didn't make enough of our corners, free-kicks and the chances we created. That's why we lost the game.
"It's very damaging for our position in the league and difficult to swallow."
Wenger added: "The table is the table.
"We have lost two big games in the last week, and that's very damaging for us.
"We cannot afford to drop points any more if we want to be in the top four."