The top-of-the-table clash between the Reds and Red Devils could not live up to its billing as both played to cancel each out.
Liverpool started the game on the front foot but failed to muster up a real chance to score as they lacked attacking fluidity and allowed the visitors to grow into the game.
Manchester United had chances during the dying embers of the game to inflict Liverpool’s first home defeat of the season but Alisson Becker was there to save the hosts on several occasions.
"It's only a good result if we win the next game,” Solskjaer said after the game.
"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 were stronger towards the end. We didn't start at all in the first half. We didn't have any composure or try to impose ourselves.
"The team is working hard for each other.
"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.
He added: "Fair play to them - with two central midfielders at the back and to defend as well as they did shows their quality."
"I think we grew in the game and towards the end it was there for us to win. We created two massive chances and it was two brilliant saves by the keeper.
"We can play better than this, we can be more composed, we can have the ball more and we had to defend really often. There are a couple of things for us to improve on
"I thought Paul (Pogba) was absolutely brilliant today. We knew he had to do a job defensively to help us with Robertson and I thought he was excellent and should have gotten the goal his performance deserved."
