Jurgen Klopp's side have yet to win a game in three attempts this season – the German manager's worst start since take over at Anfield in 2015.
Liverpool had 17 shots on goal with five on target in Monday's game – one more than United – and Klopp felt his side had done enough to take all three points.
“We should have won this game, I know it sounds ridiculous but that is how I saw it,” he said. “I am concerned about our situation, but that is how it is.”
They have been hampered by an injury list that has included Naby Keita, Diogo Jota, Ibrahima Konate, Joel Matip and Thiago Alcantara – while new striker Darwin Nunez is serving a three-game ban after being sent-off against Palace.
“It's been a bit of a difficult start,” Liverpool forward Luis Diaz admitted.
“It's not quite the outset we wanted for the season. We're a club that goes out to win three points from every game we play.
“I wouldn't say it's problematic for the players or for the manager but certainly we all know we need to do better.”
You can see the Liverpool squad training on Merseyside ahead of Saturday's game in the gallery above. To move on to the next photo, click on the arrows or if using a mobile device, simply swipe.