The Blades went down 3-0 - their fifth defeat in six league matches - and remain second from bottom in the table, six points adrift of safety with nine games remaining, but their travelling support impressed Steer at Vicarage Road.
Steer said: "It is the way we are really, our supporters are among the best in the land. The backing from our fans on Saturday was simply terrific.
"It was also the same when we beat Forest in the last home game. The fans were there throughout and I'm sure it will be the same when we take on Leeds. I was so impressed by the loyalty the fans showed to the club and the players at Watford."
Steer added: "I cannot thank our supporters enough for sticking with us through these difficult times on the pitch. It is something I appreciate, as does the management team and the players."