The Norwegian has also pointed to “long balls" that he suggests make the Reds the most direct team in the Premier League.
Solskjaer said: “We have just had a game against the best team in the country at the moment.
“I felt the last half-an-hour we could take something from the game, yes.
“When we weathered the storm in the first 10 minutes of the second half, I felt we created chances and put pressure on them.
“It doesn't matter whether the scoreline is a fair reflection of the game. They won it. We had chances and they had chances. It's about taking the moment. We had some big chances but Liverpool will say they deserved to win.
“They are the most direct team in the league. They put you under so much pressure and I thought our defenders and midfielders handled it well.
“When the long balls go for Mane, Salah and Firmino, then it is very difficult as they always look to go in behind you.
“The last 10-15 minutes we really pressed them back and made them look tired and us look really fit.
“We looked strong. But we didn't have that quality. When you don't have that quality in the last pass and finish then you aren't going to get anything from places like this."