The Cumbrians slipped back down toward the relegation zone after goals from Charlie Daniels, Scott McGleish and Simon Church before Scott Dobie late consolation strike, leaving Abbott fuming.
"Missing chances is part of the game but what we can't afford to do is not show determination to support and win the ball back quickly, get to second balls and pass," Abbott said.
"We were ragged and two of the goals we conceded were pathetic. That was a poor performance and it's difficult to explain it.
"The fans are frustrated. They want to see determination, honesty and commitment and that's what I am looking for now.
He added: "We have to stand up and be brutally honest. We can't hide and duck the issue. That performance has made me angry and it's something that has to be rectified."