The Red Devils offered an honest assessment of the "cagey" contest at Anfield after the final whistle
Harry Maguire has admitted that Manchester United were left "disappointed" with their result against Liverpool after the top-of-the-table clash largely failed to live up to the pre-match hype.
United missed the chance to open up a six-point lead over Liverpool after being held to a 0-0 draw by the defending champions on Sunday .
Both sides struggled to create chances in a game which saw Liverpool boss possession while the Red Devils tried to pick them off on the counter, with the likes of Bruno Fernandes, Marcus Rashford, Mohamed Salah and Roberto Firmino all putting in subdued performances.
Fernandes and Paul Pogba squandered the best opportunities of the game late on as Alisson protected the home side's 68-game unbeaten record at Anfield, while Fabinho and Jordan Henderson also shone as makeshift central defenders for Jurgen Klopp's team.
Maguire has insisted that United set out to get three points instead of one, but he wasn't completely satisfied with their attacking display against their arch-rivals.
"They started better than us but second half we came into it a lot more. We created the best chances and on another day we win," the Red Devils defender told Sky Sports .
"It was cagey. Two good teams matching up. We created openings and had two great chances, two great saves.
"There is a lot of talk of Liverpool being without their first-choice centre-halves but they've had a great defensive record since these injuries. They have lots of options.
"We wanted to win. You could see our intent in the second half, we wanted three points. We'll feel a bit disappointed. It's a tough place to come.
"You can see our performance compared to last year when we weren't brave at all. We were a bit timid."
United are now only top of the standings by two points ahead of second-placed Leicester, who beat Southampton 2-0 at the King Power Stadium on Saturday.
Solskjaer will now start preparing his players for a midweek trip to Fulham, while Liverpool have a home fixture against Burnley to look forward to a day later.
The Reds will be aiming to bring a four-game winless streak to an end against the Clarets, having slipped to third in the table.