The Sky Blues dominated mustering 17 corners and 21 attempts on goal compared to the Blades' six and four.
However, they failed to find a way past United goalkeeper Steve Simonsen who denied them on several occasions - while Gary McSheffrey hit the bar twice with free-kicks and blazed over a late chance.
Blades boss Adams admitted his side had good fortune but was delighted with the overall defensive display.
Adams said: "We rode our luck at times but in terms of defending when we had to we were excellent, particularly from corners and free-kicks and especially in the first half.
"In the second half I thought we came into the game a little bit and probably had the best chance of the game to nick it - and it would have been nicking it to be fair.
"I was delighted Steve Simonsen kept a clean sheet because it is demoralising for a keeper to keep seeing the ball in the back of the net."
Welcome to the Yorkshire Post's exciting match-day service, called Match Centre. Here you will find minute-by-minute updates, stats and team formations. Plus reports from every game in England, from the Premier League down to the Blue Square Premier.
Simply select your game from the pull down menu, then click on the 'i' information button on the right of the fixture and it will give you access to everything you need to know about your team.
So if you can't make it to a game, head for the Match Centre and we will give you the best seat in the house. Click the link below.
For the latest team news, score and commentary from your team check out our new Match Centre
For previews and interviews read Saturday's Yorkshire Post and for full reports and analysis read Sports Monday, free inside your Yorkshire Post.