The Brazilian missed the 1-0 victory at Anfield with a back injury amid a third Barcelona bid - that boss Jurgen Klopp refused to confirm or deny - but is reported to be worth around €124million.
But what was apparent during a difficult 90 minutes was that the Reds were missing that spark of creativity that Coutinho has to unlock packed defences as they struggled to breakdown a compact Palace defence that had shipped three goals at home to newly-promoted Huddersfield Town on the opening day.
Klopp either needs the playmaker back on the pitch - particularly for games such as this when they didn’t have a player capable of making a killer pass - or to reinvest quickly in his squad before the transfer window closes at the end of the month.
He made five changes from the side that started the Champions League win over Hoffenheim in midweek, with Roberto Firmino and Daniel Sturridge in central attacking roles but neither looked particularly threatening.
Fortunately Liverpool do have Sadio Mane, whose speed and awareness was enough to secure the three points when he seized on poor Palace defending to prod home the only goal in the 73rd minute.
Mane was again Liverpool’s biggest threat and substitute Mohammed Salah stretched the Eagles when he came on shortly after the hour, but the travelling fans regularly asked Anfield: “Where’s your Coutinho?” and Klopp is the person that needs an answer to that most.
“At the moment, as you can imagine, it’s not too easy for anybody, but we have to be concentrated on the job on the pitch, and I really think the boys did brilliant,” he said.
“I don’t think that it makes sense to think too much ahead, what can happen and when.
“The situation is like it is, and it has not changed, that’s all I know. When there is no other decision possible - on the 31st of August - then we have to think about everything new.”
Liverpool insist they won’t accept any offer from the Spanish giants but, should that change, it was expected they would spend a sizeable chunk on centre backs.
Joel Matip and Ragnar Klavan started against Palace and stood firm - mostly - but ex-Red Christian Benteke still had a glorious opportunity to make it in an incredible fourth successive win at Anfield.
The Belgian international has scored more goals at the stadium as a visitor than he did during his brief stop at the club and he could have added another memorable strike had he not blazed horribly over the bar from close range after good work from the impressive Ruben Loftus-Cheek.
Liverpool’s young fullbacks Joe Gomez and Andrew Robertson did at least impress. Robertson, making his full debut, got forward well, sending in two dangerous crosses that Matip and Mane failed to turn goalwards and then went close with a 25-yard strike himself that Wayne Hennessey tipped over the bar.
“We need to have the opportunity to do something like this [to make changes] and when the players then play like this it’s the best reaction they can show,” Klopp said.
“Everybody can now see how good Robbo – with a few more sessions – can be, especially in offensive situations. His crosses are a real threat.
“When we think a little bit about how we would feel playing our first game at Anfield, you cannot be full of joy because there’s a lot of pressure on yourself. He did really well.
“And Joe, no surprise. Even when he was a long time injured, a difficult time for him, there was no doubt about his quality.”
The defeat leaves Palace without a point in an early Premier League table but boss Frank de Boer was at least encouraged by side’s improvement after an awful first game.
And the Dutchman expects his squad to improve before the end of the month.
“We are still looking. If we think that there is the chance to inject quality into the squad we won`t hesitate, but it has to be the right one and we will not panic buy,” he insisted.
Mignolet 7, Gomez 7, Matip 7, Klavan 7, Robertson 8, Henderson 6, Milner 6, Wijnaldum 6 (Solanke 71, 6), Mane 7, Firmino 6 (Lovren 90), Sturridge 6 (Salah 61, 6).
Hennessey 7, Fosu-Mensah 7, Dann 7, Tomkins 6, Ward 7, Milivojevic 6 (Kaikai 77, 5), Puncheon 6 (McArthur 73, 5), Van Aanholt 6 (Schlupp 84), Loftus-Cheek 8, Townsend 7, Benteke 6.