Doncaster boss Sean O'Driscoll saluted Billy Sharp, while Bristol City assistant Keith Millen felt they deserved a point.
On-loan striker Sharp, who is with Rovers for the season from Sheffield United, found the net for the fifth successive game in the 12th minute.
He capitalised on some slack defending from the Robins as the home side secured their third victory on the spin
"Brilliant," O'Driscoll said. "We have a striker in form. Goals change people's perceptions, but he has played exceptionally since day one.
"He is just bright and breezy and works hard. He likes a physical confrontation, gets battered and bruised in training and gets on with it. When you have a happy player you get performances.
"He doesn't let anything upset him. He is a good asset. I think the crowd like him and the players appreciate him as well. If he gets chances he takes them."
There has been speculation that Sheffield United might recall the 23-year-old but O'Driscoll added: "He is on recall to sell, so they can't recall him unless they have a good offer for him and want to sell.
"Give me £2million and I'll sign him."
The visitors were far stronger after the break and even had a goal ruled out when Danny Haynes was ruled offside.
"Someone has told me that when the ball was hooked back in he was onside," said City assistant manager Keith Millen.
"If that's true then it's frustrating, but if you take that away we still haven't worked their keeper enough."
City have now lost three times in five games and Millen added: "After Tuesday (when they beat Leicester 3-1) we were looking to build on that and unfortunately we took one step forward and then went two back.
"In the first half we matched up against them. We made one mistake and Billy Sharp has punished us.
"We penned them in for long periods in the second half but never really had the quality of balls forward or creativity to make chances.
"That said, I would say we deserved something. A draw would have been a fair result but you have to give Donny credit.
"For us, we need to create easier chances. We are making it too hard for ourselves."