The Premier League champions rarely tested Reds keeper Simon Mignolet and looked to to be overran in midfield for large parts of the game.
The Red Devils drew 0-0 with Chelsea and beat Swansea 4-1 in their two opening Premier League fixtures, but Moyes believes his side's performance in defeat against Liverpool was the best of the lot.
"I thought we played really well, probably the best we have played this season. We just couldn't quite find the final ball or the right finish," he said to reporters, after telling BBC Sport: "From what I saw today, I'm more than happy with what I've got. I wouldn't be worried if I didn't add to the squad."
With United chasing Ander Herrera, Marouane Fellaini and Daniele De Rossi, as well as, according to reports, Luka Modric and Ilkay Gundogan, the Scot could not give an indication as to whether he would be able to bring in midfield reinforcements before Monday's 23:00BST transfer deadline.
"There isn't very long left," he added. "I couldn't give you a heads-up at the moment."
Moyes also revealed that Wayne Rooney will miss three weeks of action after sustaining a head injury in training on Saturday due to a collision with Phil Jones.