Thiago Alcantara agreed with Jurgen Klopp that Liverpool must prove they deserve to be in the Champions League next season.
Mohamed Salah gave the Reds the lead in the third minute and the hosts were on top throughout the clash but they were ultimately punished for not taking their chances.
An extra minute was added for a VAR decision which had ruled out a Callum Wilson goal in stoppage time and on-loan Arsenal man Willock took full advantage.
The unconvincing performance did little for Reds boss Klopp’s hopes of restoring the club’s battered reputation in the wake of the Super League controversy and even less for their top-four aspirations.
And speaking after the game, Thiago was unable to describe the disappointment inside the Liverpool dressing room.
He told BT Sport: “We have no words to explain the disappointment we have. The will to win, the desire to win is a very big part of the competition. We had a lot of chances to win in the first half.
“We tried to play our game. That was the key today. It worked very good in the first half, we created many spaces and created a lot of chances.
“It doesn’t change that we want to win and want to be in the Champions League but for that we have to deserve to be there.”
Klopp also said his team have to learn if they are to achieve a place in next season’s Champions League.
He told BT Sport: “I don’t think you can create many better chances than we did. We scored a wonderful goal but didn’t finish the game off.
“They deserved the goal because they had scored before…we didn’t even take the present. We were lucky with VAR today and gave another chance away, it makes no sense and it’s really tough to take. Why it happened I don’t know.
“It’s a point but it feels like a defeat. Today I didn’t see that we deserved to play in the Champions League next year.
“We have another five games and we will see what we can do. We learn, or we don’t play Champions League.”