Fans questioned the board's decision to offer Abbott a new 12-month deal in May after the Cumbrians had flirted with relegation during the previous campaign when they finished 17th.
The Cumbrians home defeat to Port Vale on Saturday left them without a win from their first six league games this season and the club confirmed Abbott's contract had been terminated on Monday.
"The contract extension was agreed in May of 2012 when we agreed then that we would extend the contract by a year," managing director John Nixon told a press conference.
"This was a contract that was effectively going to run out in 2013 in June and we decided a year earlier we would extend it and we weren't going to change that having made the decision and having given our word.
"It wasn't something that was decided in the summer and it wasn't something that was done under the pressure of fans' opinion and it wasn't something that was done in light of having a poorish season last season.
"We don't think it was a mistake. The decision was taken in May of 2012 and at that point in time we finished eighth in the league and we had every confidence going into last season that we'd build on that and push on for promotion.
"The back half of last season was significantly better than the first half and so absolutely, we had no thought at all that we had made the wrong decision."
Nixon added the board wanted to have a new manager in place in time for the away game at Stevenage on September 21.
Assistant boss Graham Kavanagh and youth team coach David Irons will take charge of the first-team for Saturday's home game with Sheffield United.
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