First-half goals from Steve Guinan and Ben Smith were enough to earn the Bulls a precious three points and move the Cumbrians perilously close to the drop zone, despite Michael Bridges' strike for the home side.
"I'm not going to hide from anybody. We are low at the minute and we have to find some sort of optimism between now and Saturday," Abbott said.
"It's a serious situation and a serious knockback to us because it was a game we expected to win.
"That was typical of what has been happening to us in the last few games. We never do things easily and we shot ourselves in the foot again which is very disappointing.
"Hereford capitalised on our mistakes but we had enough chances to win three games. They were clinical in the first 20 minutes and that left us with a big hill to climb."