Liverpool manager Brendan Rodgers has told his players they must learn to handle the extra expectation that comes with being a Champions League club.
The Reds' 3-1 defeat at West Ham was their third loss in five league games.
It is only the second time Liverpool have experienced that as a top-flight club in 77 years.
"There is a new expectation at the club. Teams have always wanted to beat us but we are even more of a rival now. We have to deal with it," said Rodgers.
Liverpool returned to the Champions League on Tuesday following a five-year absence, beating Bulgarian side Ludogorets Razgrad 2-1 at Anfield.
But the Reds were below par at Upton Park, falling two goals behind inside seven minutes as they struggled to cope with West Ham's vibrant attacking play.
Those strikes from Winston Reid and Diafra Sakho were followed by a Raheem Sterling strike for Liverpool, but the hosts sealed the victory late on through Morgan Amalfitano.
The result leaves Liverpool 10th in the Premier League, already six points behind leaders Chelsea, who have a game in hand.
|Liverpool's next four games|
|Tues, 23 Sept: Middlesbrough (h) Capital One Cup|
|Sat, 27 Sept: Everton (h) Premier League|
|Wed, 1 Oct: FC Basel (a) Champions League|
|Sat, 4 Oct: West Brom (h) Premier League|
"The group has come such a long way," said Rodgers. "The level expected now has grown. But we have to be able to cope with that and at the moment we're not.
"We arrived early last year. There is no limits on what we want to achieve but we have lost three of our five games. We need to get back to that level as quickly as we can.
"You can't run away from it. We were brilliant last season, but at this point last season we weren't at the level we got to at the end. We have a bit of work to do."
Hammers manager Sam Allardyce explained how he specifically focused on the fact Liverpool might be jaded from their midweek European exploits.
"Liverpool had played in the Champions League for the first time in five years, which is tiring, and we wanted to start as quickly as we could," said Allardyce.
"We said let's not let them control the tempo and press their back players. It worked brilliantly."