Bobby De Cordova-Reid gave Leicester a halftime lead before Josh Zirkzee struck for United on 68 minutes. Harry Maguire headed home the winner in injury-time, with Leicester disputing the goal for offside.
Van Nistelrooy said afterwards, "We are not defeated in Fergie time, we are defeated in offside time.
"This wasn't necessary. VAR you have in a couple centimetres, a couple of inches, this was half a metre, clear in line. That was a hard one to take because the team deserves to draw in the end. Then extra time, stay in the game you, never know what happens.
"It was a very good team performance, started really well, pressing United. On the ball very stable. Deserved to go 1-0 up at half-time. Of course we know in the second half they're going to put some pressure on us and some chances but not even that much.
"We deserved to go into extra time, go for the battle in extra time and maybe penalties.
"Decisions like these in our level are hard to swallow."