Graham Kavanagh lashed in a 30-yard stunner in the fourth minute, but Rovers were allowed back into the game nine minutes later after slack defending presented Northern Ireland international Jeff Hughes with a gift he duly accepted.
For the rest of an end-to-end clash Rovers had the edge, and only a string of missed chances prevented them from making it three straight away wins.
Abbott said: "We put them on the back foot but it was a really soft goal to concede. After that it was toe-to-toe with a lot of honest endeavour.
"We wanted to start the game well but their goal stopped us in our tracks. A bit of anxiety crept in and that is something we will have to deal with.
"It was a patchy performance. We played some great stuff at times but we need to be tougher in both boxes. At times we want to do well but make the wrong decisions."