Doncaster boss Sean O'Driscoll believed his side did not do enough to beat Sheffield Wednesday and admitted a draw would have been a fair result.
Billy Sharp - a lifelong Sheffield United fan - scored in the 78th minute to condemn struggling Wednesday to their third successive league defeat at the Keepmoat.
Sharp was on hand to convert Simon Gillett's cross midway through the second half to leave the Owls dangerously close to the bottom three.
The Rovers boss sees his side climb to 15th in the Championship table, but was quick to credit the visitors for making life hard.
"It was a very dour game and not a lot (in the crowd)," O'Driscoll said. "They came to do a job, tried to stop us from playing and credit to them.
"They worked really hard for Brian, which is what you want from your side, and it was always going to be settled by one chance, either side.
"On overall play, if we'd have walked off here with a draw I would have said 'OK'."
On-loan Sharp bagged his eighth goal of the season for O'Driscoll's men in the win, and the personal significance of the strike was not lost on the Rovers boss.
"It was a good goal for us and ironic that Billy gets it and we get three points," said O'Driscoll.
"I don't think Billy's going to miss from two or three yards. Most of his goals are scored from inside the six-yard box.
"Simon put it on a plate for him and it's ironic because he's a Sheffield United boy, so he'll be pleased he scored against Wednesday"
O'Driscoll, whose side turned around their campaign after being rooted in the bottom three for the first half of last season, said he sympathised with Laws' predicament.
He added: "I've been there. We were sitting bottom of the table this time last season, so I know what Brian's going through.
"We won't be gloating over it, but we're grateful for the three points. We worked hard for it, it wasn't one of our better performances, but they didn't allow us to play, so you've got to give them credit."
Wednesday haven't scored in seven hours of football, and never looked like finding a way past Rovers keeper Neil Sullivan.
The defeat sees their winless run extend to eight matches, but the Owls boss said he was confident his charges could turn their fortunes around.
And Laws - no doubt heartened by the passion shown by his players - remained upbeat despite the result.
"I got what I asked for," Laws said. "That was a derby-like performance. We were very dogged, hard to break down, resilient and committed.
"In the end I thought the end product let us down a little bit, but that's just confidence.
"The commitment was 100 per cent and I've said to the players it doesn't matter what happens in terms of games, if you put that kind of effort in we'll turn it round.
"We've got to believe. The supporters believe we can do it, they were outstanding."
The Wednesday manager saw his side create very little, and he quickly acknowledged the difference between the two sides - match-winner Sharp.
"We know what Sharp's all about," he admitted. "He gets in the six-yard box and if the ball comes in he scores.
"All his goals come from the six-yard box and that's where he was tonight. That's why you pay a lot of money for that and I'm sure Doncaster would love to keep him."