James Collins netted in between Andy Williams' double before substitute Raffaele De Vita completed a 4-0 rout for the Robins.
Carlisle's travelling fans called for Abbott to be axed after the final whistle at the County Ground.
Abbott restricted his post-match comments to a minimum after admitting he found few positives to take from the heavy beating.
He said: "I was very disappointed with the result and the way we played.
"We were beaten by a good side. Swindon are a good side, so let us leave it at that.
"All I am prepared to say is that there are positives and negatives in every game, so there is nothing more to be said."
- Sports & Recreation
- Raffaele De Vita