The Scot was enthused by his side's resounding victory in Germany, which came courtesy of Antonio Valencia, Jonny Evans, Chris Smalling, Nani and an Emir Spahic own goal.
Strikes from Antonio Valencia, Jonny Evans, Chris Smalling, Nani and an Emir Spahic own goal comfortably defeated Sami Hyypia's side and guaranteed the English champions a place in the knockout stages of the Champions League.
Speaking after the game, Moyes ranked the performance in Germany as the best he's seen since replacing Sir Alex Ferguson in the summer and praised his side's defending after a third clean sheet in four games.
The Scot told reporters: "It's the best we've played in my time here and there's more to come. The goals will get the headlines but we defended well.
"For us to come away from home and score five goals is really special. There were so many great performances. All around it was a great performance from the players.
"That is what I was hoping to get more often this season.
Shinji Kagawa and Wayne Rooney starred in attacking roles for United, although Moyes reserved special praise for the midfield performance of Ryan Giggs, who turns 40 on Friday.
"You cannot question him as a football player," he added. "He didn't look fatigued for his age at all. There are signs that we have been getting better."
Giggs, meanwhile, enjoyed his role operating in front of the back four and believes the Red Devils could have added more goals on the night against the side currently second in the Bundesliga.
"We really killed them on the counterattack and it was a pleasure to play behind the front four," the Welshman said. "In the second half we could have scored more goals but to score five goals anywhere in Europe is brilliant."