The Cumbrians were just a goal down when they lost skipper Lee Miller to a red card on the half-hour mark and they never really recovered from that upset.
O's, who led 2-1 at half-time, went on to win convincingly and have now scored a total of 13 goals against Abbott's men in their last three meetings.
However, Abbott said: "I'm still optimistic for the season, but we have to play with a full complement of players. Whatever I say will make me angry and frustrated. I didn't see a red card from where I was. We lost our leader, captain and talisman and it's difficult once he's gone."
Abbott added: "Our back four has got to be tougher. We are hurt and damaged. Orient have a savvy nastiness that comes with experience and this is a brutal league.
"It's a bad result and I have got the difficult job of picking things up, but I will stand up and take responsibility for it."
Abbott found a sympathetic ear from counterpart Russell Slade after Orient's convincing victory.
Slade said: "I feel for Greg, who is a good friend of mine, because with all the preparation you do you can't legislate for that first half and Miller getting sent off.
"We were at the top of our game, but I'm sure Carlisle will be fine. Things conspired against them and I'm just happy to get that first win under our belts. We have taken the first step, but there's still a lot of work to be done and I thought we showed our adaptability."