But Ward kept United's hope of promotion alive with an opportunist set-piece at the death.
They flattered to deceive at times, particularly after the interval, but Blackwell applauded their single-mindedness and determination.
"I thought it was going to end in frustration," he said. "But we got the result that we deserved.
"You have to win football matches in lots of different ways and we did that.
"We played some terrific stuff at times, some scrappy stuff and some ugly stuff. But we got there and rightly so."
Blackwell added: "Jamie's free-kick is something we work on in training so it was good to see that pay off.
"We ask the lads to put the ball in a certain position because it's horrible for the goalie to come (out). Then, if it's on target, there's a great chance that it will go in. And it did."
United, who climbed to seventh in the table, dominated in terms of territory and possession but failed to put Preston goalkeeper Andy Lonergan under any real pressure during a tepid, low-key encounter.
Just seven months ago, these two teams contested a pulsating play-off semi-final but on this evidence appear unlikely to trouble the Championship's top six next May.
Ward saw a speculative effort blocked by Neill Collins as United seized control of the opening exchanges while Henri Camara, making only the second start of his Bramall Lane career, dragged wide after a smart turn on the edge of the box.
Even referee Trevor Kettle had seen enough and, after half an hour, limped off with a hamstring strain.
Things did not get any better until Ward finally made United's dominance pay four minutes from time.
Sean St Ledger, making his first appearance for Preston since returning to Lancashire following an unhappy spell at Middlesbrough, capped a superb individual display by scrambling Richard Cresswell's header off the line midway through the second half.
But St Ledger's efforts proved in vain when Ward curled a free-kick over Lonergan and inside the far post to ensure United's persistence received its reward.
Preston manager Alan Irvine said: "I thought we had earned something from that.
"We looked comfortable towards the end and, if anything, seemed the more likely to go on and do something.
"It was a terrific delivery from Ward to score but my lads are adamant that it wasn't a free-kick in the first place.
"We knew we had to stand up to United because this is a very difficult ground to come to.
"The one thing we could have done is use the ball much better."