It worked, as a much-improved second-half display from the Blades saw them salvage a point in a 1-1 draw at the Banks's Stadium.
Craig Westcarr gave Walsall a 44th-minute lead with a low shot from James Baxendale's cross.
Febian Brandy missed a hat-trick of decent chances before the Blades grabbed a point when Kevin McDonald's shot was turned onto a post by goalkeeper Sam Johnstone, and substitute Chris Porter tapped in the rebound.
Wilson said: "It was a game of two halves. We never got a grip of it in the first half and quite honestly we looked anxious and didn't handle the pitch well, and allowed them too much space.
"There were one or two choice words at half time because I was very angry with that performance.
"The second half I got a response and we really took the game to them, and I think we deserved a goal. Walsall had a couple of chances but they are a very good side with some tricky and quick players.
"A point is better than none and we must be grateful for small mercies. I think it was a fair result in the end.
"Our two substitutes (Porter and Callum McFadzean) did very well in the second half and Porter showed what he is capable of doing."