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."
Doncaster boss Paul Dickov was unhappy with his side's first-half performance, in which Rovers failed to produce a shot on goal, but was pleased with their improvement after the break and praised the impact of match-winner Macheda.
Dickov said of the Italian loanee: "He comes alive in the box. He's got that horrible knack of being in the right place at the right time, which is what every team needs and every team wants.
"At the minute it's still just the month (his loan deal) but we're hopeful we can extend it. All the conversations that we had when he first came in were really positive."
Dickov, who saw his side win for the first time in seven matches, added: "In the first half I was really disappointed with the performance. I thought Wednesday were better than us with and without the ball, but we're going to get days like that.
"At half-time we changed the system around and in the second half we were a lot better. We kept the ball better and we were a threat on the break as well.
"I'm delighted with the three points more than anything else because we've been playing well recently and not getting the points we deserved, so to pick up three away from home, we're really happy."