Midfielder Liam Noble grabbed a goal in each half to give the Cumbrians victory at the Keepmoat Stadium on Tuesday night 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.
"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."