The Cumbrians got away to a blistering start with two goals inside the first 13 minutes from Rory Loy and a Lee Miller penalty as Stevenage went down to 10 men with the dismissal of goalkeeper Steve Arnold before Marcus Haber replied for Boro midway through the first half.
Loy was making his first home start in over 12 months after recovering from a broken leg.
Abbott said: "We are in a good place right now. It's taken an exceptional amount of hard work to get our season moving in the right direction and everyone has put in a shift to move the club forward.
"A lot comes from within the club and every goal and point breeds more confidence and the crowd come expecting us to get a result now."
Although the win did not improve Carlisle's league placing, Abbott added: "The season is far from over and we have a lot of points to play for.
"The only blip on the day was the fact that we let a goal in because that can spread anxiety. It's a bit nervy when you are only one goal ahead although (goalkeeper) Mark (Gillespie) did not have a lot to do."