The Hammers saw their perfect start to 2021 brought to a halt by the champions on Sunday as Mohamed Salah scored two stunning goals at the London Stadium before Georginio Wijnaldum added a third late on.
Craig Dawson then scored his second goal in as many games but it was too late for the hosts, who lost 3-1.
Coming into the game off the back of six straight wins across all competitions, West Ham were unusually nervy on the ball and lacking conviction in the first half before being picked apart by sheer quality in the second.
West Ham remain just four points off the Champions League places, but Moyes says a lack of quality and composure will serve as a reminder of just how good they need to be.
“It was tight,” Moyes said. “We found it hard against Liverpool. We were better in the first half but didn’t show enough composure at times against a really good side.
“We have been in good form. We came into the game with a lot of confidence. This is the difference, at this level it shows. We’re trying to catch a few teams up, not Liverpool, that’s for sure.
“The players have been excellent. Even today, it’s a lesson for them – the levels we have to get to. We didn’t do the things we usually do well today.”