It was the third successive goalless draw at Bramall Lane for Wilson's promotion-chasing Blades.
Jonathan Forte came closest for the home side, but he scuffed wide when well placed in the 67th minute.
The visitors played the final 16 minutes with 10 men after defender Sean O'Hanlon was dismissed for two bookable offences.
Wilson said: "We have to do better and if it's going to be a scrappy one-nil, then we'll take a scrappy one-nil.
"I think the 10 men, it just pulled everybody tighter with Carlisle; they didn't look to play out at all then."
Wilson added: "We've got to be concerned because we're not winning at home.
"Our best results, in recent times, have been away from home.
"Maybe there's a bit of anxiousness around and that's understandable, but we have to turn that into a positive for us and not worry too much about it.
"We've got to try and break teams down and keep plugging away at them. It's difficult, but you still keep going and you can't get too disappointed with it."