Daniel Sturridge struck in the fourth minute to maintain Liverpool's 100 per cent start to the season, leaving United with just one win from their opening three fixtures.
The defeat raised plenty of questions about the squad depth at Old Trafford, but Moyes refused to be drawn on reported bids for Everton's Marouane Fellaini and Athletic Bilbao star Ander Herrera, adding that his players impressed him, regardless of the loss.
He said: "We'll continue working for what we have left (of the window) to get what we can in, but I was really impressed with the players today. I can see why they were champions.
"I think we played really well, we just couldn't get that last bit to score. With the exception of the opening few minutes when we gave away a bad goal, it was probably the best we have played all season."
Moyes could only look on in frustration as his side struggled to break down a stubborn Liverpool side, only managing to test Simon Mignolet in the home goal with four shots on target.
Despite that, Moyes was happy with his side's attacking prowess and rejected claims that United would have fared better with Alex Ferguson in charge.
"It wasn't for the want of trying or the lack of attacking players on the pitch trying to get them to score," he continued.
"It would have been a tough ask even if Sir Alex was in charge. This is undoubtedly a really big fixture for both clubs and to play Chelsea is undoubtedly a really big fixture.
"I think we have maybe not come out of the three matches with as many points as we'd like, but we've shown we are in good shape and maybe (it is) a little unjust (for us) not to be seen up there with a real chance of winning the championship."
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