The Sky Blues dominated, mustering 17 corners and 21 attempts on goal compared to the Blades' six and four.
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."
Source: PA
Source: PA