The Reds came into the match looking to build upon their excellent start to the season and could have gone level with Manchester City and Arsenal at the top of the Premier League with a win.
However, Jurgen Klopp's men never got in to their stride as they were stifled by a United team determined to take something from their trip to Anfield.
A forgettable first half was punctuated by just one opportunity, Jordan Henderson delivering an excellent cross to an unmarked Roberto Firmino at the far post, only for the Brazilian to head straight at David de Gea.
The game threaten to open up after the break, Zlatan Ibrahimovic missing a golden opportunity to put United in front against the run of play when he got the timing of his header from a Paul Pogba cross all wrong.
Liverpool then came on strong for a brief period, Emre Can bundling his way through the visitor's defence but his low effort was well kept out by De Gea.
Coutinho was the next to be frustrated by the United shot stopper as he did brilliantly to push away the Brazilian playmaker's long range effort.
The introduction of Adam Lallana gave the Reds more impetus but they were unable to find a way through a solid United backline as Jose Mourinho once again managed to frustrate the Anfield faithful, two-and-a-half years on from his Chelsea side ending Liverpool's title hopes.