Headers from Danny Ings and Sam Vokes gave Burnley the lead at half-time but were pegged back after a David Prutton header on 70 minutes.
The Owls continued to press but the Clarets held on for all three points to leave Jones' men without a win this season.
"We started okay, we then had that lull in the first half where nothing seemed to stick with us and our passing was a bit awry and they capitalised but we should have stopped the crosses and defended the crosses better," Jones said.
"It became an uphill battle in the second half, we've come out and had a right go and if we had a little more luck we might have come out with something from the game and it's frustrating but we're a bit stretched at the moment.
"We know we can do better and we will work at it but we know as well we have two inexperienced full-backs but you can't blame them for the goals today and collectively we should have done better.
"I couldn't fault them in the second half, I didn't want them to go into their shells and hide.
"I've said to them from now until the end of your careers you'll make mistakes, it's how you react to that mistake."
Sean Dyche felt his Burnley side deserved the three points although they did not reach the heights they have recently.
Dyche said: "Another performance with good productive moments, I don't think it's as good as we have played and we were close to playing well in the first half. We scored two very good goals I must say, very good bits of quality.
"In the second half we knew they would come back at us, they have got a big physical presence and we had to match that or be better than that.
"I felt the biggest turning point was an unbelievable not given penalty which, quite frankly, if we score then I think that the game's done and it flattens the crowd. Over a season you hope there's a balance of it, but it changed the feeling of the game.
"They came back at us stronger, got it forward even quicker and we had to make sure we dealt with it and overall we did.
"In the end was a small moment in a big game but it could have been a big moment and another big moment was Tom Heaton's double save so very pleased with that as well. "