The Merseyside outfit maintained their 100 per cent start to the campaign thanks to another match-winning goal from Daniel Sturridge as United failed to score in successive Premier League games for the first time since 2007.
And Moyes accepted Rooney's absence with a cut head - a problem that is likely to keep him out for three weeks - was a contributing factor.
"Wayne would have made a difference today," said Moyes.
"We maybe lacked something different at times.
"But we didn't have him because of the injury."
Rooney suffered a severe cut to the head following an accidental collision with Phil Jones in training on Saturday.
Without the England forward - who will now miss his country's crucial World Cup qualifiers against Moldova and Ukraine - United failed to exert any significant pressure on Liverpool.
Robin van Persie cut a particularly frustrated figure as Moyes' inability to win at Anfield stretched to 13 games, 12 of which are a legacy of his time at Everton.
Yet the Scot remained remarkably upbeat afterwards.