Southampton boss Ralph Hasenhuttl to BBC Sport: "I think we conceded a stupid goal shortly before half-time. Then we had a big chance for 2-1.
"On the counter-attack it's 1-2. From that our heads are going down and a team with this quality kills you immediately.
Crystal Palace boss Roy Hodgson: "It was always going to be a tough opening fixture for us, but I am really pleased with how we approached it.
"I have to take my hat off to our goalkeeper for making a fantastic save, but I am very happy to get off to a good start against a team like Southampton with such good quality.
Southampton manager Ralph Hasenhuttl told BBC Sport: "I saw a team in the second half that is really showing how every part of their game is developing. We had strong offensive moments, and solutions against these teams is not easy, but we deserved this win today.
Bournemouth manager Eddie Howe speaking to BBC Sport: "In some ways it sort of mirrored our season.
"It was a really cruel twist. We worked so hard to create the chances we needed and you think in that moment you've been rewarded.
Southampton manager Ralph Hasenhuttl: "At half-time it was a disaster, we were not the team you have seen in the last weeks in the first half. But we played much quicker, made the right decisions and it was a good game in the second half.
Manchester United boss Ole Gunnar Solskjaer, speaking to Sky Sports: "It was the worst time to concede a goal but it happens in football. We have won so many games in that way. It is all part of the learning for this team.
Southampton manager Ralph Hasenhuttl said Che Adams' first goal for the club was "so important for him"
"When you hear how much the guys were celebrating him as he went into the dressing room, then you know how happy they are he scored," Hasenhuttl said.