Livesey, 27, who has signed a new one-year contract with the option of another 12 months, will start his eighth campaign with the Cumbrians in August and is convinced Greg Abbott's side can build on last season's eighth-placed finish.
"I think we learned a lot from what we went through last season and we're going to be able to take those lessons into next year," the centre-half told the club's official website. "Hopefully we'll do better because of it.
"We know if we can add a little bit in terms of depth to the squad then we're going to be in with a real chance. Our aim has to be the play-offs, if not better, and I know the lads will be pushing for that from day one.
"It's another reason why I wanted to stay. We came really close to getting into the play-offs and I have thought for a while that it would be crazy to leave when we're getting ready to have another good go at it.
"It was hard to take when we started to realise that we'd left ourselves with a bit too much to do but, like I say, you've got to take the disappointment and learn from it as much as you can. Next season we can use this experience and make sure it doesn't happen again."