The top-of-the-table clash did not live up to the hype, as these games so often do.
The Reds dominated possession in the first-half but United came closest to scoring when Bruno Fernandes' free-kick almost beat Alisson.
Fernandes was denied again by the Brazilian before Reds midfielder Thiago came close to scoring from long-range.
The result means United two points ahead of Leicester City in second.
Liverpool, who have scored one point in their last four games, are a point behind the Foxes.
Speaking after the game, United manager Ole Gunnar Solskjaer lamented his side's inability to take their chances.
"It's only a good result if we win the next game," said Solskjaer.
"It was an opportunity missed with the chances we had, but then again we were playing a very good side. I'm disappointed, but still a point is OK if you win the next one.
"We have improved and progressed. It's not just the result we're disappointed with, it's some of the performance. I know these boys can play better.
"Fair play to them - with two central midfielders at the back and to defend as well as they did, showed their quality."