Burnley winger Keith Treacy hit the opening goal just after the hour mark, and it was his cross which Lewis Buxton handled to give away a penalty that Ross Wallace converted to complete the scoring.
Wednesday took 20 minutes to register a shot on goal with Kieran Lee's diving header being kept out by keeper Lee Grant.
And Lee's shot just before the break was blocked by Michael Duff, before the centre-half recovered to snuff out Michail Antonio's follow-up effort, in an afternoon where Wednesday struggled to create any clear-cut chances.
"I just don't think we got going," Jones said. "I think we looked flat. It was always going to take the first goal, there was nothing really happening in the first half.
"We just seemed to lack a bit of a spark and nobody seemed to get the game by the scruff of the neck. We were dropping too deep, I was screaming at them to squeeze the game.
"I don't know whether it was just one game too many. We can sort that out this week - too many players had an off day which we can't afford.
"When you look at the table a win would have put us in the pack with everyone else which would have been great, so it's an opportunity missed and we're disappointed at that.
"We needed just to stay solid and hopefully someone up the top will get hold of it. We couldn't seem to get anything going and have a sustained spell of pressure.
"Were so disappointed because we've worked so hard over a short period of time and we had a great opportunity to get three points at home and really get ourselves close to that pack."