Former Shrews midfielder David McAllister scored the only goal of the game just four minutes into United's second assault on promotion out of England's third division, but the performance was far from pretty at a sunbathed Bramall Lane.
Most Blades fans probably wouldn't have begrudged Shrewsbury of a point from Saturday's encounter, but as has been said before, it is now a results-based business.
And Danny Wilson knows that the quality of performance must be bettered to ensure the Blades get a positive consistent set of results this season, but he is just happy to get the first three points on the board.
He said: "It was a very typical first game of the season, really hard-fought, very tight, with Shrewsbury playing some really good stuff at times. It is a great three points at this stage of the season with results being a bit freakish on opening day.
"We are delighted to get the three points. I have to say that we've had the chances to put the game to bed, some very clear-cut chances, perhaps more than them. Yes there are loads of things to work on, but it's the first game of the season and it was very important for us to just get the three points.
"It wasn't necessarily a case of relief at the final whistle, we were just pleased to get off to a good start and get the momentum building up nice and early. Today had the potential to be a banana skin, as very few people expected Shrewsbury to win the game, so to come out unscathed was a bonus. However, it was a good lesson for players and fans alike that there are some good sides in this division, with some very strong and effective players in certain areas. Take last week for example, a 4-0 score line flattered Leeds."
Wilson went on to comment on individual performances, including new summer signing John Cofie from Manchester United. He continued: "We knew John Cofie would feel fatigued because he has missed some training recently but we were delighted with some of the movement from Shaun Miller when he came on. David (McAllister) took his goal really well early on and he had good game playing in a slightly less familiar position wide on the right.
"Whether or not we deserved the win is irrespective at the minute, we were just delighted to get three points."
The Blades are now focusing their attentions on Tuesday night's trip to Coventry's Ricoh Arena.