Three opening league wins have seen United go joint top, their latest success coming in midweek at Bramall Lane when the Blades recovered from 2-0 behind to win 3-2 with goals from Matthew Lowton, Lee Williamson and Richard Cresswell.
“There is a never-say-die attitude about my players, and they showed it by coming back from two-down to win against Walsall,” said Wilson.
“But there is also a warning sign there for us because we can’t get caught in a mind-set where we think we can come back from two-down on a regular basis. While it can happen once in a while, it’s not going to happen on a regular basis.
“But it is still nice to know that we have got that in our locker. Certainly, we have a real belief that we can make an impact in games whatever the situation.
“The confidence you get from winning a run of games gives you that belief that you can always win the next one.”
While youngsters Lowton and Harry Maguire may have taken the headlines from their League One opening, Wilson acknowledged the spirit throughout the Blades squad.
“Michael Doyle and Lee Williamson were outstanding when they came on as subs against Walsall, and they have been really unlucky not to have been in every starting line-up so far,” he said.
“But one of the things that has pleased me most about the season so far is the attitude shown by the players who are not in the side. It has been spot-on and speaks volumes for the spirit we have in the camp.
“They are all committed to the cause and that is great for this football club.
“Steve Simonsen has said that he was unhappy with the two goals he conceded against Walsall, and I have had to pick him up.
“But it is so difficult for goalkeepers out there on the pitch because there is no hiding place for them.
“I have been delighted with the way Simmo has performed this season. He’s a good keeper with lots of experience and he’ll bounce back.”
Wilson, who has another of his new signings, Kevin McDonald, struggling with ankle trouble, predicts a tough trip to Prenton Park, for the Blades’ first meeting with Tranmere in over a decade.
“Tranmere have got good players, individuals who can hurt you like Showunmi up front and McGurk and Devaney on the flanks.
“They are resilient and tough to break down on their own patch, and they don’t give many goals away.
“So a lot of patience and resilience will be required by us. We have got to be up for it. We must be on the ball.”