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," 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.
"We played very well," he said.
"If you look at the games against Swansea, Chelsea and today, we have played well.
"We scored all our goals in the first game, but played well, and limited teams to very few opportunities."
Moyes now has one more day to strengthen his squad, with Everton duo Marouane Fellaini and Leighton Baines remaining the more likely targets after Athletic Bilbao coach Ernesto Valverde insisted he expected midfielder Anders Herrera to remain with the Primera Division outfit.
"I'm not thinking about speaking to him to convince him about anything and I'm not worried about anything else," said Valverde following his side's defeat at Real Madrid.
"I haven't spoken with the player but what I'm going to repeat is that I don't expect the club to make any moves in the transfer market tomorrow [Monday].
"I do not know what will happen. I want Ander to stay with us, and that is what I think, expect will happen."
For his part, Moyes remains optimistic executive vice-chairman Ed Woodward, who was at Anfield for today's defeat, can make the signings he wants.
"Maybe in the next how many hours we will get a chance, but I can't give you a heads up," said Moyes.