Goals from Blades pair Ryan Flynn and Nick Blackman put their side 2-0 up and although defender Danny Livesey pulled one back for Carlisle in the second half, Neill Collins tapped home a third for the visitors.
Abbott admitted that the number of goals being conceded at home - 28 in 11 games - was damaging his side's league position.
He said: "I'm upset at the amount we're conceding, but I will turn it round and we'll keep working as hard as we can to try and get the results that we need.
"Sheffield United are a top team and we asked a lot of questions, but we gave away a soft third goal when it could have been 2-2."
Once again Carlisle's defensive problems, which had seen them lose their last three home games, resurfaced in the 16th minute as Blackman's cross from the right was allowed to reach Flynn at the far post and he was left with the simple task of prodding the ball past goalkeeper Adam Collin.
Blades increased their lead in the 34th minute when Blackman skipped past Bradley Potts and, from the tightest of angles somehow managed to squeeze his shot through Collin's legs.
There was a big improvement from Carlisle after the break and twice in the space of a minute the Cumbrians were unlucky not to pull a goal back.
First Liam Noble's lob from the edge of the area hit the crossbar then substitute Dave Symington's low raking 25-yarder bounced back into play off the post.
Carlisle got their reward in the 71st minute when Livesey's header from Jon-Paul McGovern's corner found the top corner and Blades goalkeeper George Long kept out a thunderous free-kick by the 18-year-old Symington before the Blades went 3-1 ahead in the 84th minute through Collins.