The Anfield club found themselves 2-0 down after just six minutes at Upton Park as Winston Reid and Diafra Sakho capitalised on some slack defensive work to score.
And, though Raheem Sterling's goal before the break gave Liverpool a lifeline, the hosts repelled further attacks before Morgan Amalfitano broke away late on to clinch the three points.
Rodgers' side have now lost three of their opening five Premier League games this season, and the boss believes a lack of intensity is to blame.
"West Ham will be delighted, they played well," he said. "I've got to look at my own team and, for us, we were nowhere near the standard today.
"We made a really slow start and before we knew it were two down. Lots of elements of our game have been very good over the last couple of seasons but it's not really happening for us at the moment.
"So we've got a lot of work to do. Today was very disappointing in terms of performance."
The visitors' performance was in stark contrast to that during their last trip to London, a 3-0 victory over Tottenham at White Hart Lane.
And Rodgers suggested that the absence of the likes of Daniel Sturridge and Joe Allen - both of whom are currently injured - has had a huge effect on his team's effectiveness.
"I think we showed the potential in the Tottenham game this season," he added.
"When we have players fit, we showed in that game the real quality and intensity of the team. When those guys aren't available it can really hurt us.
"We still should be better than what we were today so there's no doubt we need to go back out on the training ground and continue to work.
"We've set a new expectancy at the club, which we have to deal with now. We've got lots of games and Liverpool as a football club is a club teams want to beat but we have to deal with that and we will do."
