The Cumbrians have failed to win any of their last five home games and host Scunthorpe on Saturday on the back of a 3-1 reversal against Leyton Orient on Tuesday.
The defeat caused Abbott to brand his team's defending as "pathetic" and he now challenging them to rectify matters against the Iron.
"The fans are frustrated," he told the News and Star. "They need to know that I won't accept that and the players shouldn't be prepared to accept it.
"What the fans want to hear is determination, honesty and commitment. That will be enough for me on Saturday. We have got to face everybody and be honest with the situation.
"We have got to take it head-on and come out all guns blazing on Saturday."