Sam Hewson twice came close to putting United ahead in the first half, while former Liverpool striker Robbie Fowler spurned the visitors' best chance after eight minutes.
England international goalkeeper Ben Foster was substituted after 57 minutes after sustaining a badly twisted ankle, but replacement Ron-Robert Zieler was in sharp form to preserve the Reds' clean sheet.
Defences were on top for both sides, but there was still plenty of attacking verve and promise in United's display, only for the final ball to be their undoing time and again.
It was veteran forward Fowler who had the first opening of the evening, but he could only fire over the bar with a powerful first-time effort. It was Fowler's main contribution before his half-time substitution.
Sam Hewson had the Reds' two best efforts in the first half. First his long-range effort was well clutched by Blackburn goalkeeper Mark Bunn, then the midfielder's powerful diving header just cleared the bar in the 40th minute.
United's first effort of note after the interval came from Danny Welbeck, who fashioned space on the edge of the area before curling an effort into Bunn's midriff.
Foster was substituted just before the hour mark, landing awkwardly on his right ankle after coming a long way to collect a lofted Blackburn free-kick.
The Reds' stopper did not seem too peturbed, smiling as he left the field. Replacement Zieler