Rovers' on-loan Manchester United striker Federico Macheda headed the only goal of the game in the 71st minute, his third strike in two games, as Wednesday's winless start to the Sky Bet Championship season stretched to eight games.
Miguel Llera's 63rd-minute header, which Rovers goalkeeper Ross Turnbull turned around the left-hand post, was as close as the Owls came as they failed to score for the first time this season.
Jones said: "We dominated it, sometimes a little lack of quality in good areas, but we've had some good chances, half chances to score.
"I think they've cleared a couple off the line, the keeper's made a great save from Miguel (Llera) and it's frustrating.
"It's hard for everybody at the moment because if you play poorly and lose you've got to accept it but when you've given everything.
"You've got to just keep fighting and digging in and we won't allow anyone to feel sorry for themselves.
"I thought we tried to work it, we tried to play it. We had some good positions in the first half without really testing them but that's the final bit; the bit of quality you need in and around that box.
"We certainly got in and around the box lots of times but they had lots of bodies and threw their bodies on the line."
Jones added: "I can accept (conceding from) a set-play but I can't accept the goal we gave away. I think people do have a responsibility to deal with that and I don't think we dealt with it.
"We can't allow someone to score four yards out, centre of goal."