The fans half feared it, the pundits shook their heads and even the club had doubts, but when it comes to juggling the demands of the Barclays Premier League and European competition, while Fulham are coping magnificently, Rafael Benítez’s team are not.

The fragility of Liverpool’s season was never starker. Benítez is having to calculate how many minutes he can squeeze from his top players without exacerbating their various injuries. It is no way to run a team who were, at the end of last season, among the favourites to win the title and to reach the final stages of the Champions League.

The maths for Benítez are becoming more intricate by the hour. It is clear to the least medically minded that Fernando Torres needs a rest; a proper legs up, TV on, cuppa at the ready rest. But, because he is not as hampered by injury as some of his team-mates, the striker has to feature.

Benítez has always been noted for his scientific method, but the amount of complex mathematics he has to contend with is bordering on the ridiculous.

The 80 minutes that Torres played against Manchester United at Anfield resulted in the Spain forward needing four days of rest. So, children, heads down, turn your exam papers over and calculate how many minutes he should have been allowed against Fulham if he is to be fit for the match against Lyons on Wednesday.

Benítez and his staff decided the answer is 63, but only on Wednesday will we find out if that was the correct calculation.

Of course, there would be little in the way of furrowed brows and calculators if Benítez could rustle up a bench brimming with precocious talent and impressive experience. But he cannot. Perhaps the most telling element to this defeat was that Roy Hodgson, the Fulham manager, had to contend with two injured players — Diomansy Kamara and Damien Duff — at half-time but their replacements were, if anything, more influential.

Fulham can travel to Rome for their Europa League match on Thursday buoyed by a dream victory. So how does Hodgson get the balance right between domestic and European demands?

“You don’t, it would be naive to believe you can get it right,” he said. “The fact is, both competitions are such enormously difficult competitions to win. The moment you dilute your chances of winning one competition by trying to win the other one, it makes life much more difficult. You get injuries because players don’t get the time to recover.”

“Tell me about it,” Benítez might have muttered, having seen Torres warm down after the game, looking extremely uncomfortable as he did so. Surely there must be a temptation to give him a long rest rather than juggle spurts of recuperation with playing time? But Benítez is aware that to have kept a partially fit Torres on the bench would have left him open to even more criticism.

The carefully computed moment for the departure of Torres came with the game poised at 1-1 and though Torres was clearly not functioning at full pelt, he was Liverpool’s most potent threat and his withdrawal must have affected the morale of those left on the pitch.

Fulham took the lead against the run of play, shortly after Yossi Benayoun had hit the crossbar. Bobby Zamora darted, as if invisible, between Emiliano Insúa and Sotirios Kyrgiakos to connect with Duff’s cross.

For all Liverpool’s possession — 74 per cent — they created few real threats and their equaliser came as a consequence of a ricochet that fell at the feet of Torres, who reacted with almost frighteningly quick reflexes to fire past Mark Schwarzer.

Philipp Degen and Jamie Carragher were dismissed within three minutes of each other in the second half, but Fulham had already regained the lead. Dirk Kuyt, with his customary zeal, elected to keep the ball in play acrobatically, but inadvertently set up a Fulham attack that was finished by the neat clip of Erik Nevland’s heel. “There was a bit of a mix-up out wide and once you go down to nine men it is virtually impossible,” Carragher said.

Fulham proceeded to have fun against depleted opponents and sealed victory when Clint Dempsey almost lazily ran to meet Nevland’s through-ball.

Benítez disputed both red-card decisions. Degen can make a strong case that he should have been merely cautioned for his foul on Dempsey and Carragher claimed he reached the ball as he tangled with Zamora. But although luck is not on the Liverpool manager’s side, some of the club’s fans trudged away wondering why Benayoun had been left to shuttle away thanklessly on the flank when he would have thrived operating directly behind Torres.

Even so, in spite of the bedraggled mess Liverpool appeared at the final whistle, few of those fans would bet against the team rising to the seemingly impossible challenge of reaching the knockout stages of the Champions League once again.

Fulham (4-4-2): M Schwarzer 6 J Paintsil 6 A Hughes 6 B Hangeland 6 P Konchesky 6 D Duff 6 C Baird 6 J Greening 6 C Dempsey 6 R Zamora 7 D Kamara 5 Substitutes: E Nevland 7 (for Duff, 46min), Z Gera 7 (for Kamara, 46), D Etuhu (for Greening, 86). Not used: P Zuberbühler, S Kelly, B H Riise, C Smalling. Next: Wigan Athletic (a).

Liverpool (4-2-3-1): J M Reina 5 P Degen 5 J Carragher 5 S Kyrgiakos 5 E Insúa 4 J Mascherano 6 Lucas Leiva 5 Y Benayoun 5 A Voronin 5 D Kuyt 5 F Torres 7 Substitutes: R Babel 4 (for Torres, 63min), N Eccleston (for Benayoun, 78), D Ayala (for Kuyt, 84). Not used: P Gulacsi, J Spearing, D Plessis, A Dossena. Next: Birmingham City (h).