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.
Southampton manager Hasenhuttl to BBC Sport: "There were tears in my eyes - because of the wind! When you see our guys fighting with everything they have it makes me really proud. You need to have the perfect game against Liverpool and I think we did have that.
"We didn't get the result we wanted but it's not the worst thing in the world and there are worse things happening," Klopp told Amazon Prime.
"But I liked the game - we are not happy with the result but I'm fine with the performance because that's the way we have to play and protect.
Liverpool manager Jurgen Klopp: "It does feel like a defeat, but we have a point more than before so it is completely fine.
"It's our fault but they deserved the point. In the first half it looked like 90:10 possession - it's a massive challenge to stay on track and do it again but we should have done it.
Crystal Palace captain Luka Milivojevic to BT Sport: "It's hard to speak after a defeat like that, they were so clinical.
"They punished every mistake, opened the game well, we were in it after that and had chances.
Fulham boss Scott Parker to BBC Sport: "I feel a bit disappointed. The players do as well. It shows how far we've come.
"There were two different halves. The first half, we were every bit of what we needed - commitment, energy, desire, passion.
Liverpool captain Jordan Henderson to Match of the Day: "The first half there were one or two things we could improve on. We maybe should have scored the second. Overall we have to be happy with the performance.
Manchester City boss Guardiola speaking to BBC Match of the Day: "It was a tight game. We struggled in the first minutes because they had four players up front. Mane and Salah were playing between the lines, then we adjusted after and had more control.
Sheffield United manager Chris Wilder speaking to BBC Sport: “No hard luck stories, you have to go again. We have had opportunities. You are not expected to dominate at Anfield, but we did more than enough to get something from it and we are disappointed we are going back on the coach with nothing.
Liverpool manager Jurgen Klopp told Match of the Day: "Performance-wise very, very happy. Best away game we've played here since I started managing. We gave away two goals on set-pieces after changing formation.