Midfielder Liam Noble grabbed a goal in each half to give the Cumbrians victory and end Rovers' six-match unbeaten home run.
Abbott said: "The lads were terrific - every one of them right through the team. They all did their jobs and stuck to the game plan against a difficult team on a difficult surface."
He added: "The last thing we wanted was to concede an early goal and we defended superbly right from the start. Without being disrespectful to Doncaster we looked comfortable and won a tad comfortably in the end.
"I'm pleased for Liam Noble because he's not shown off his best in the last few games but he can be a top player if he develops other sides of his game.
"He was top drawer in this game. In fact, the midfield was really dominant and the effort and determination we have shown in the last few games has been tremendous."
Doncaster boss Brian Flynn remained upbeat despite the defeat and said: "We started the game strongly but all credit to Carlisle for making it difficult for us.
"They were very energetic and stopped us playing before grabbing a goal from a deflection and then the second one put a different complexion on the game.
"We started the second half brightly as well but it just wasn't our night.
"I'm not just writing it off like that but it's not the end of the world and the league table will look the same in the morning because nothing has changed with two of our rivals losing."