Craig Conway pounced in the 80th minute to send the Bluebirds back to the top of the Championship as Wednesday stayed in the relegation places.
Jones, returning to his former club for the first time since they sacked him last year, said one lapse cost the Owls dearly.
"We switched off at that vital moment," he said. "The only time we've switched off in the whole of the game was when (Joe Mason) has laid it off and we didn't come out quick enough to block it.
"They worked so hard but that has happened to us too many times this season when they've worked hard and had that lapse of concentration at certain times in the game.
"That is four or five times that has happened to us and today was another one.
"We've frustrated them and probably had the best chance of the game to have gone 1-0 up and had a couple of half chances. We knew they were going to pummel our box and look for knock-downs.
"Unfortunately they took that chance when it came around and we didn't."