THE Sky Blues fell to defeat at Bramall Lane thanks to a goal right at the start of the second half.
But, after falling behind to Richard Cresswell's strike, City had the better of proceedings but couldn't force an equaliser despite pushing late on.
It was a quiet start to the match with both teams looking to work each other out. Chances were few and far between in the opening half hour with both keepers having little to do.
But as the first period wore on, the Sky Blues started to get a foothold in the game with David Bell providing a couple of good crosses from the right.
Keiren Westwood made a fairly simple save to deny Darius Henderson before Leon Barnett made a great block and then tackle to keep out United's Glen Little.
Coventry won three corners around the half-hour mark but United managed to see-off the threat.
In the 35th minute, Westwood made a good save at full-stretch to keep out Andy Taylor's low shot from long range.
Barnett produced more impressive defending two minutes before the break. Henderson looked certain to score with a header but the City defender managed to block and then had the presence of mind to throw himself in front of the rebound to put off the striker.
United ended the half strongly with Stephen Quinn going close from the edge of the box but shot just wide.
And the Blades took the lead immediately after the break. Little set up Cresswell on the edge of the City area and he shot past Westwood into the top corner.
For a moment, United threatened to add to their advantage but City regained their composure. In the 55th minute, Coleman sent on Freddy Eastwood in place of Freddie Sears in a bid to get back into the game.
Sammy Clingan fired a free-kick over the bar on the hour mark and two minutes later Carl Baker shot low but it was comfortable for Steve Simonsen to save.
The Sky Blues made a real fist of grabbing an equaliser. Richard Wood headed a Clingan corner goalwards but it was cleared from just in front of the goal by Paul Connolly.
Aron Gunnarsson broke from midfield but his shot was blocked by Nyron Nosworthy and then Eastwood fired over the top from the edge of the box.
Coventry had a great chance to draw level when Simonsen picked up the ball after James Harper's hook. Clingan cracked over the bar from Michael McIndoe's tapped free-kick from ten yards.
Eastwood carved a shooting chance for Gunnarsson in the 90th minute but the Icelandic international fired over from 20 yards.
Sheffield United: Simonsen; Connolly, Morgan, Nosworthy, Taylor; Little (Williamson 74), Montgomery, Harper, Quinn (Yeates 82); Henderson, Cresswell
Subs: Naysmith, Bennett, Seip, Bartley, Geary.
CoventryCity: Westwood; Wright, Wood, Barnett, Cranie (Clarke 84); Bell, Gunnarsson, Clingan, Baker (McIndoe 64); Morrison, Sears (Eastwood 55).
Subs: Hall, Konstantopoulos, Grandison, Jeffers.
