Colchester took a 51st-minute lead when Martin Rowlands played a one-two with Steven Gillespie and finished superbly, but Carlisle midfielder James Berrett secured a point for his side midway through the second half when he latched o nto Tom Taiwo's flick and broke clear to score.
Abbott said: "We've half a chance of the play-offs. If we keep playing like we are, keep our performance levels and determination, we'll keep upsetting people and that's what we want to do.
"I thought the first goal would be massive, but we actually played very, very well after that and deserved our equaliser.
"Their goal was a terrific goal, to be fair but our's came from a fantastic move. Our performance more than deserved a point. This is a difficult place to come as they don't get beaten here very often.
"But we've competed well and made life difficult for them. We might just have done enough to keep Colchester away from us and winning and not losing games breeds confidence. I'm really pleased with the players and the way they are approaching games"
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