Kolo Toure headed against a post, while Daniel Sturridge, Philippe Coutinho and Raheem Sterling failed to break down their second tier visitors despite relentless pressure.
Aston Villa -- who beat West Bromwich Albion 2-0 on Saturday -- are the only side to seal a semi-final spot so far while Manchester United host holders Arsenal on Monday.
Giant-killers Bradford City travel to Reading on March 16 for a replay after their 0-0 draw.
"It's been difficult here against Championship teams, Blackburn deserve credit," Liverpool manager Brendan Rodgers told BT Sport.
"But my players also deserve credit, they were missing sharpness but they kept going and tried to create chances."
While third tier Bradford had captured the imagination with their march to the quarter-finals, Blackburn had gone about their business quietly in dumping out Premier League Swansea and Stoke before they arrived at Anfield.
Pre-match renditions of 'You'll never Walk Alone' had barely ended when Liverpool lost their defensive rock Martin Skrtel.
The Slovakia defender contested a header against Blackburn's Rudy Gestede but fell heavily on his neck and, after an eight-minute delay, was carried off on a stretcher. Liverpool had lost just one of their previous 21 games in all competitions but Blackburn coped comfortably in the opening stages and led by the powerful Gestede were carving out opportunities of their own.
Craig Conway spurned the best chance of the opening period, blazing high and wide from close-range.
Sturridge's rasping shot in first half stoppage time drew a smart stop from Blackburn keeper Simon Eastwood.
Immediately after the break the hosts were indebted to goalkeeper Simon Mignolet who produced a wonderful save to palm away Alex Baptiste's header but thereafter Liverpool were dominant.
Toure hit the post and Sturridge became increasingly influential though he was thwarted by Blackburn's determined rearguard.
Liverpool laid siege to Blackburn's goal in the closing stages but failed to force Eastwood into many meaningful saves.
"It was 90 minutes of concentration because they had a lot of the ball and they had some great players out there," said Blackburn captain Matthew Kilgallon. "It was just about concentration and working for each other."
(Reporting By Tom Hayward; editing by Martyn Herman)
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