Manchester United manager Solskjaer said: "They are a good side and they have some injury problems but we didn't pounce on that.
"I felt we grew into the game and got stronger and stronger and were closer to winning.
"We were a bit disappointed in the performance, not just the result. We didn't do well enough to cause them problems in the first half but we defended well and they didn't create too many chances."But I think everyone was a bit disappointed with the way we started the game but that is a good feeling to have - that we were disappointed in the performance."
Liverpool boss Klopp told BBC Sport: "The performance was good and the first half was exceptionally good.
"With all the things that were said before the game - United are flying and we were struggling - and then to play this kind of game, I was happy with that.
"We tried in the second half again, but you cannot deny United over 90 minutes, not with the counter-attacking threat they have. So they had two really good chances, I have to say, but we had our chances in the second half as well.
"The way we understood the game, the way we felt the game, the way we read the moments were really good. But it is not exactly how it should be so we have space for improvement, absolutely. We will keep working on that."