The managerless Blades, four points off the relegation zone, face four league games in nine days, starting with the home clash with Hull on Boxing Day before successive trips to Norwich and Burnley and a derby clash with Doncaster at Bramall Lane on January 3.
Britton told the club's official website: "With the gaffer (Gary Speed) going during the week and it being a difficult week and JC (John Carver) taking over, it was nice to get the win.
"There's a lot of games coming up now and a good chance for us to pick up. There's a lot of points on offer in a short space of time and this is a chance for the team to put a run together and if you do that you'll shoot up the table."
The Blades confirmed earlier this week they will not be appointing a new manager until early in the new year following Speed's departure to become Wales coach.
Source: PA
Source: PA