Molby seems to suggest a more methodical and thinking approach from the visitors compared to Liverpool, who seemed to let the occasion get to them.
In his Liverpool Echo column, Molby said: "We built this up as a big game we needed to win desperately while United probably prepared themselves in a much more pragmatic way.
"They treated is as just another game. They let their heads rule their hearts. And they won.
"That’s not the first time we haven’t been able to get over the line in a big game in the last few years.
"Sure, there are big demands from the crowd. But you need to manage yourself as a player and that’s possibly where we struggle a little bit. We used our nervous energy in the wrong way instead of channelling it positively."
It could prove to be a costly defeat for Liverpool in their bid for the Champions League places as Manchester United opened up a five point gap with just the eight games remaining.
United became the first side in 2015 to overcome Liverpool and made themselves strong favourites to return to the Champions League after only one season's absence.
It was certainly an impressive display from the visitors last Sunday as they put in a commanding performance at Anfield, and their away record certainly seems to improving, giving them vital momentum in the final part of the season.
Molby anticipates it will be difficult for Liverpool to close that gap now, and a big game against Arsenal over the Easter weekend could be make or break. Win and they go within three points of the Gunners, lose and they could be eight points behind the Champions League places with just the seven games to go.