The Hammers lost 3-2 after fighting back from Glen Johnson’s 11th-minute opener with a Mark Noble penalty and a Steven Gerrard own-goal allowing them to take the lead early in the first half.
Joe Cole notched a long-awaited Premier League goal in the 76th minute before an unfortunate own-goal from James Collins gave the Reds the win and Alalrdyce was left to rue what may have been.
"We were never in control of the game completely especially against a side like Liverpool, we were not going to dominate for the whole game," he said.
"We gave everything we could. We can't continue to play and dominate teams we play, when we did today we got ourselves in the lead.
"We just got promoted, we are in a good run of form and there are expectations from fans.”
West Ham dropped to 11th on the table with the third loss in four matches whilst Liverpool grabbed a second victory on the trot to move up to 10th.