The Millers, who are unbeaten in 15 games, are five points behind second-placed Brentford going into the final few weeks of the season.
The Bees travel to Bramall Lane on Tuesday night for their game in hand knowing a win would probably kill off the Millers' chances of overhauling them.
They are without a victory in two though, including a 3-0 defeat at the New York Stadium last week - but Evans expects Mark Warburton's side to prosper.
"I hope that Sheffield United are good enough to beat Brentford, we were good enough, I don't think they will be," he said.
"That's taking nothing away from Nigel Clough because what a job he has done, but I'll be the first to acclaim them if they manage it.
"I hope they do, I'll be there watching them and it will be the only time in my career that I have played for Sheffield United because I'll be kicking every ball with them.
"We have had three big mountains in a week, going to my adopted town Peterborough and getting a win, nobody has spoken to me in that city since," he laughed.
"It was a magnificent performance, the best in a while, against Brentford and I think we matched that in the first half against Bristol City.
"This dressing room makes me, the chairman and the fans believe. They continue to set expectation levels, no one else."
Source PA