Blades manager Gary Speed drafted in Sunderland midfielder Reid in time to make his debut off the bench in last Saturday's 1-0 home defeat to Coventry, the fourth time United have lost a league game at Bramall Lane this season.
Britton, a free summer signing from Swansea, said: "Andy Reid is quality. He has played in the Premier League and has got a great left foot.
"You could see how comfortable he is on the ball as soon as he came on and I'm sure he will prove his quality over the coming weeks."
Britton added: "The lads have got to stick together as a group. We aren't far off, so we have to keep believing in each other and turn things around through sheer graft and belief."