Match winner Jose Baxter and Jamie Murphy acknowledged Crawley Town pushed the Blades all the way at the weekend.
John Gregory's Red Devils gave a good account of themselves in South Yorkshire and only a last-ditch block from Chris Basham prevented former Blades loanee Izale McLeod from nicking a point with one of the last kicks of the contests, but Murphy felt the Blades deserved all three points.
The Scotsman, who played in a number of attacking roles on Saturday, commented: "I think we shaded the first-half, but just lacked that bit of quality in the final third.
"Crawley had their chances in the opening 45 minutes and one at the very end, but I thought we defended well and a clean sheet was crucial.
"We knew we needed to start brightly after the break and it was a fantastic effort from Jose, he does that regularly in training, so it was no surprise to see the ball sail into the net from that range."
Baxter, who curled home a delightful goal to settle the fixture early in the second-half, echoed Murphy's sentiments, but comended the efforts of the Sussex based outfit, adding:
"It was a tremendously weighted ball by Craig (Alcock), all the pace was on it and thankfully I made a clean contact and it gave the goalkeeper no chance.
"It was a really hard fought clash as we knew it would be, but we defended well and putting your body on the line at the back is as important as scoring at the other end.
"It was a real team effort, a deserved win and hopefully we can now go to West Ham and cause a shock in the cup."