But if that is the case, the neutral will hope for a far less one-sided affair - as Liverpool attacked relentlessly but lacked the necessary guile to open the scoring.
Rafael Benitez's Liverpool side will take on Atletico Madrid after overcoming Benfica 4-1 at Anfield to win 5-3 on aggregate, while Fulham won 1-0 at German champions Wolfsburg for a 3-1 aggregate victory and will face Hamburg in their last-four encounter.
But, there were no signs that Liverpool were feeling the effects of their exertions in the week as they started brightly with chances falling to David Ngog, Maxi Rodriguez and Aquilani.
The home side had received an attacking blow prior to kick-off when talismanic 22-goal striker Fernando Torres was ruled out with a knee injury.
And Liverpool missed the Spanish international's cutting edge as they dominated, Ngog lashing a half-chance high and wide after being put through by Javier Mascherano early on.
Benitez admits defeat in race for fourth
Liverpool found joy down the flanks and an inventive piece of play by Aquilani almost brought the opening goal.
Glen Johnson's cross was headed back across goal by Steven Gerrard and Aquilani, with his back to goal, teed himself up an overhead kick but the shot flew straight into the hands of Schwarzer.
Seconds later Maxi was set loose in the box but he fired into the feet of the impressive Fulham stopper.
Schwarzer was again tested by Mascherano, who found space 25 yards out and looped a vicious half-volley towards goal which the keeper just managed to palm away to his right, as Liverpool threatened to run riot.
Hodgson delighted with Fulham persistence
Despite their stunning form in Europe, Fulham have not won on the road in the Premier League since the opening day of the season and their lack of attacking intent at Anfield gave an inkling as to why.
A double chance for Aquilani at the start of the second half suggested the second period would again be dominated by the home side.
First the Italy international's curled effort from 20 yards was touched over the bar by Schwarzer, before Aquilani drove a left-footed effort wide.
Fulham continued to defend deep and invite Liverpool on to them and Babel took the opportunity to test Schwarzer again with a fierce low drive which was pushed around the near post.
It began to feel like it would not be Liverpool's day when Greece defencer Sotirios Kyrgiakos headed over the bar when he really should have done better from five yards out after being set up by Dirk Kuyt.
Liverpool missed Torres - Carragher
And as the seconds ticked by Liverpool could not find the urgency or ingenuity to carve open the robust Fulham defence leaving the Anfield crowd frustrated and having to contemplate next season without Champions League football.
The result may also mean that if these two sides do meet again this season it would represent Liverpool's best chance of taking something out of a disappointing campaign.
Liverpool manager Rafael Benitez:
"I am a little bit disappointed, normally when you control the game and have chances you can score. We know the fourth position is a little bit far away.
"They were deep, they were well organised and we had to score. We had one or two chances, their keeper was good, but it's not easy to find space when they have players behind the ball.
"We needed to be patient and it was not easy to find the final pass in the final third.
"I am disappointed because I feel that we had plenty of possession."
Fulham boss Roy Hodgson:
"There is no doubt Liverpool dominated the game and we were forced on to the back foot but at the same time we stood our corner very well and fought very hard.
"We stopped them getting clear-cut chances and it was really when we just lost Daniel Agger for a corner at the end that I was concerned the ball was going to go in the back of the net.
"On the occasions when they got good strikes in Mark Schwarzer was equal to it. It is another excellent clean sheet.
"I have got to be very satisfied with what the team has done because Liverpool are a very difficult team to take points off home or away."
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