The visitors saw off a late recovery by Carlisle to complete a double over them, having beaten the Cumbrians 4-2 in a league visit a month earlier.
First-half goals from Wes Fogden and Eunan O'Kane set up the win for Bournemouth and although Mark Beck's header gave Carlisle some hope, the outstanding Marc Pugh clinched it for the south-coast men in time added on.
"I'm frustrated, but the simple fact is they had better players than us and we could not bridge the gap," Abbott said.
"The first goal was a joke goal and we are not getting the breaks at the moment. We need our key players back and to get back our belief. But no-one is going to give me a Ronaldo or a Messi and it means we have to work harder."
Once again Carlisle looked defensively fragile at home. They have won just twice for their own fans and Abbott added: "Every goal stems from someone not doing their job properly."