The Cumbrians have won just one of their last seven league matches, leaving them just four points above the drop zone.
And Livesey admitted he sympathises with the club's supporters, saying apologies "aren't enough any more".
He told Carlisle's official website: "We're all just very disappointed really. It's rapidly becoming a blame game because we know that people can't keep making the same mistakes.
"The problem we have is that it's someone different every week and I include myself in that. We've all got to start doing our jobs, it really is as simple as that.
"There is only so long we can keep saying that it will be right next week. It gets to the point where you have to start digging people out a bit."
He added: "I totally agree with the grumbles from the fans. People aren't coming - but why would they when we're getting beaten like this every week? It's up to us to get them back and to keep them here."