They let slip a 3-2 lead with three minutes to go before losing 4-3 at Peterborough on Saturday.
The Red Devils must now beat Coventry in their final game to stay up.
However there is plenty at stake because Coventry need a point from the game to remain in League One.
Saunders said: “We have one more chance this Sunday against Coventry City and fans can play their part.
“I would be delighted if as many of our fans took the time to send the players a message to show how much you are behind them and the club on Sunday.”
Centre-back Aden Flint says Bristol City’s “superb” team spirit was the single biggest factor in their League One promotion and Johnstone’s Paint Trophy double-winning season. The Robins achieved automatic promotion with three games of the campaign remaining and clinched their first league championship in 60 years. Flint insists neither of those things would have happened had not he and his team-mates been prepared to work hard for one another. Flint said: “Our team spirit has helped us massively. The spirit here is the best I’ve ever experienced and been involved with.
Nigel Clough believes Sheffield United’s big-game experience can help them secure promotion to the Championship.
The Blades enter Sunday’s final match of the League One season against Chesterfield assured of a play-off place following last weekend’s draw at Leyton Orient.
And boss Clough, who has led them into the semi-finals of both the FA and Capital One cups since taking charge 18 months ago, said the knowledge acquired during games against Hull City, Tottenham Hotspur, Southampton and QPR could prove crucial.
“We’re hoping that our cup experience will work to our advantage,” he said. “That, after gaining it, we can out it to good use. It’s always a little bit of a lottery in the play-offs but we’re hoping we’ve got enough to cope.”