With four matches remaining, the gap between Liverpool and Manchester City in fourth place is now six points and they still have to overtake Tottenham in fifth.
This afternoon of soft spring sunshine and one-sided football was the day Rafael Benitez's "guarantee" that Liverpool would re-qualify for the wealth of European football's premier competition ran out.
"It will be very difficult to make fourth place; it is not in our hands and maybe the gap is too much," the Liverpool manager conceded. "You have to support your team but you have to be realistic. You have to keep going but it is clear it will be more difficult. Maybe it is too much, Manchester City have a game in hand – and that is against Tottenham."
The irony is that in recent weeks, against Portsmouth, Sunderland and Benfica, Liverpool had been performing at Anfield with the kind of verve that had accompanied their second-place finish last season. Here, they so dominated Fulham that Pepe Reina was first required to make a save in the 91st minute.
Perhaps 55 games into a season that began in July, Fulham could be forgiven their lethargy. If this were a taster for next month's Europa League final in Hamburg, it is unlikely to match the Beatles' performances on the Reeperbahn in the early 1960s.
Had Fernando Torres been fit, Liverpool might have found a way through the massed defensive ranks. However, Benitez's greatest gift to Liverpool was seeing a specialist in Barcelona about the recurrence of the knee injury that has hampered his season. Liverpool had not failed to score at Anfield since December 2008, 37 matches ago, and this was no time to break that sequence.
Fulham have never won at Anfield and, exhausted by the victory over the Bundesliga champions Wolfsburg that allowed them to join Liverpool in the Europa League semi-finals, their ambition to break that pattern was limited. Before Roy Hodgson took over, Fulham's role in the Premier League seemed to be to travel around the country dispensing three points. These days, they are a different proposition. They still have only a solitary away victory this season – and that at Portsmouth – but this was their seventh draw on their travels.
"It was a sterling defensive performance against a very good team," Hodgson reflected. "There is no doubt Liverpool dominated the game but we fought our corner very well and to go from Wolfsburg to Anfield and get another clean sheet was a great achievement. But, if we didn't have a goalkeeper who commanded his area, we would have lost this game."
That goalkeeper was Mark Schwarzer, whom Hodgson thought underrated at Middlesbrough, but who has earned plenty of plaudits in this campaign. Apart from one moment when Ryan Babel burst into the area and drove in a hard, low shot that the Australian would have seen late by his near post, the saves Schwarzer was required to make were good rather than great.
There were, however, plenty of them – an overhead effort from Alberto Aquilani, a fierce drive from Maxi Rodriguez, and one from distance from Javier Mascherano. In the second half, Sotirios Kyrgiakos directed a free header into the Anfield Road End.
Perhaps the key moment was Andre Marriner's failure to dismiss Jonathan Greening, who, already booked, bundled over Glen Johnson 10 minutes before half-time.
Liverpool (4-4-1-1): Reina; Johnson, Carragher, Kyrgiakos, Agger; Rodriguez, Aquilani (Kuyt, 65), Mascherano, Babel (Benayoun, 72); Gerrard; Ngog (Pacheco, 79). Substitutes not used: Cavalieri (gk), Lucas, Degen, Ayala.
Fulham (4-4-2): Schwarzer; Baird, Hughes, Hangeland, Konchesky; Duff, Murphy (Dikgacoi, 76) Etuhu, Greening (Riise, 83); Nevland, Zamora (Okaka, 68). Substitutes not used: Zuberbuhler (gk), Kelly, Shorey, Smalling.
Referee: A Marriner (West Midlands).
Booked: Liverpool Carragher; Fulham Greening, Murphy, Duff.
Man of the match: Schwarzer