The Blades sacked David Weir earlier this month and have now gone through seven different permanent managers in six and a half years, while John Carver and latterly Chris Morgan, twice, have been installed as caretaker bosses during that time.
The club took a major gamble when they sacked Wilson in April with just seven seven games of last season remaining, but failed to reach the play-off final after losing to out to Yeovil in the semi-finals.
"At this stage it looks a perilous position, but I genuinely believe they will be fine and they will make an appointment in the next week and get things back on track," Wilson told talksport radio.
"I know it's a cliche, but they really are too good to be in that position, but they need stability, confidence and trust.
"Sometimes it just doesn't click (with a manager). The club is needing stability, trust and patience to get through the tough times.
"There has to be stability at clubs and that always starts with the management.
"They're the first ones who feel the weight of bad results.
"David has felt that early in his fledgling career. It can be very tough at times, it's demanding and instant in football nowadays.
"He has brought very good players in there. Had they stuck with him, would results have turned round? I think they possibly would have done."
Wilson feels he was harshly treated by the club and was confident at the time of his dismissal that promotion remained a realistic target.
"At the time I thought it was strange to dispense of me at that stage of the season," he added.
"I thought we had a great chance of the play-offs if not automatic promotion as we had two games in-hand at one stage. But that's football. You have to accept that people think change is the best thing to do."
Morgan will take charge of his second game since Weir's departure against former boss Micky Adams' Port Vale on Saturday.
The Blades, rooted to the bottom of the table, have not won since the opening day and will be chasing their first victory in 14 games in all competitions.