The Reds had numerous opportunities to beat their fellow Europa League semi-finalists Fulham but, without the cutting edge of the injured Torres, drew a blank at Anfield.
They also came up against a goalkeeper in good form in Mark Schwarzer, who produced a number of saves including a fine stop from a powerful Ryan Babel drive.
Torres scored twice in Thursday's stunning victory over Benfica but left the field early to rest a knee injury.
Manager Rafael Benitez had expected the striker to be fit but he failed to even make the bench.
Dirk Kuyt and Lucas - Liverpool's other two scorers on Thursday - also had to make do with places among the substitutes along with Yossi Benayoun as Benitez made four changes.
David Ngog, Alberto Aquilani, Maxi Rodriguez and Babel were the men to come in but none made the difference against a resolute Fulham side.
Liverpool dominated possession throughout and Jose Reina, fresh from signing a new six-year contract, barely had a shot to save.
Yet their dependence on Torres was again all too evident.
Fulham were able to boast their leading scorer and hero of their European run, Bobby Zamora, following a fitness test on an Achilles injury, but the England World Cup hopeful endured a quiet afternoon.
The Reds should have taken the lead with just three minutes on the clock after Babel won a corner.
Steven Gerrard swung the ball in from the left and it was headed back towards goal by Daniel Agger after touching a Fulham defender.
It fell invitingly for Babel inside the six-yard box but the Dutchman failed to make any connection with a volley.
Gerrard created a chance for Ngog with a superb crossfield ball into the area but the Frenchman had to stretch and volleyed wide.
The tone for most of the afternoon was set with Liverpool much the livelier side but meeting continual frustration in the final third.
Another good move by Liverpool saw Gerrard pull back a Glen Johnson cross for Aquilani, who then flicked the ball up and attempted an overhead kick but Schwarzer saved comfortably.
Moments later Rodriguez took the ball down in the area to shoot but Schwarzer blocked.
Babel then delivered a good cross for Aquilani but the Italian headed over.
Mascherano tested Schwarzer with a powerful 30-yard drive just after the half-hour but the Australian saved well to his right.
Greening, already booked, was fortunate to escape a second yellow card for blocking Johnson 10 minutes before half-time as Liverpool continued to dominate without breaking through.
Liverpool pressed on and created three good chances for Aquilani after the break but the former Roma midfielder was unable to take any of them.
The first he scuffed weakly at Schwarzer before winning a corner with a shot the keeper palmed over the bar.
The ball came to him again soon after but this time he sliced wide from 25 yards.
Fulham spent large spells defending on the edge of their own area as Liverpool continued to push but they did so manfully, getting plenty of players behind the ball.
Gerrard got in a shot on target but Aaron Hughes blocked and Daniel Agger volleyed wide.
Schwarzer also seemed unbeatable, producing a brilliant save low to his right to keep put a fierce drive from Babel, cutting inside from the left.
Liverpool attempted to freshen up their attack by introducing Kuyt and Benayoun midway through the second half while Fulham withdrew the isolated figure of Zamora.
Kuyt was straight into the action and picked out Sotirios Kyrgiakos with a good cross only for the Greek to head over.
Another substitute, Daniel Pacheco, also had a powerful effort blocked.
Time ran out for Liverpool and, not for the first time this season, their supporters left frustrated.