The Premier League champions romped to victory in the Group A UEFA Champions League fixture at the BayArena, as they sealed their place in the round of 16 in style.
Leverkusen were two goals down after 30 minutes - an Antonio Valencia strike and an Emir Spahic own goal had given United the early lead - and they never recovered.
Stefan Reinartz hit the post with a header on the hour-mark but any attempts at a fight-back were snuffed out by Jonny Evans' 65th-minute goal.
And late strikes to Chris Smalling and Nani saw Leverkusen slip to third in their group and on the verge of being knocked out.
"We will require some time to let this one sink in. We made a few mistakes and Manchester United, the quality team that they are, punished us for these mistakes," Voller said.
"We didn't have enough willpower in the second half to turn the game around. It was poor. Perhaps we have too much respect against teams like this.
"Nevertheless, we can't allow ourselves to be slaughtered like this."
Leverkusen midfielder Simon Rolfes admitted his side capitulated once Evans got Manchester United's third goal.
"That was a really tough evening for us," Rolfes said.
"The second goal broke down our morale a bit although we actually had a decent start to the game. After the third goal the game was over."
Leverkusen now need to better Shakhtar Donetsk's result on the final matchday of Group A to qualify.
Sami Hyypia's side – who are a point behind Shakhtar - play their final match in Spain against Real Sociedad, who have lost all five of their group matches.
