Chelsea manager Frank Lampard:
"I thought we were great. I'm pleased because that was us again, we had a blip against West Ham and today we were back.
"Our character at half-time was important and we carried off where we left off.
"Sergio is a legend of football. I have to score when I play because Sergio scores every time," Jesus said after the game.
Guardiola told BBC Sport: "We need him. I am so glad for him because he is an incredible fighter.
Crystal Palace manager Roy Hodgson told Match of the Day: "It was a great victory. I'm full of praise for what the players did today. To firstly lose your centre-back to a challenge which the referee deems to be a red card, and then to lose a left-back in an area where we have no cover.
Arsenal interim manager Freddie Ljungberg told Sky Sports: "We started the game really well, that's how I want to play football.
"But we need to work on the transitions, we dominated and they break us too easily.
Liverpool boss Jurgen Klopp: "It was unnecessary [for the game to be nervy at the end], of course, because we had unbelievable chances. Their keeper made some good saves.
"It was difficult this game because Brighton are a good football side.
"For me Dele is not a midfield player, he is a player to play like he is playing, close to Harry. I think this is the best position for him," added Mourinho.
"He's the best thing that can happen to a coach because everybody speaks about him, you [media], the fans speak about him for the right reasons.
The former Millwall and MK Dons keeper sank to his knees before celebrating in the stands with his father, who played in the West Ham defence for 21 years.
"It still doesn't feel real," said Martin, who is a boyhood fan.
Watford manager Quique Sanchez Flores said he "suffers" for the fans, players and owner after defeat at fellow strugglers Southampton.
The Saints came from behind to win with late goals from Danny Ings and James Ward-Prowse, easing the pressure on their own boss Ralph Hasenhüttl and leaving the Hornets bottom of the Premier League.
Newcastle manager Steve Bruce told: "It took them a wonder goal for all the possession they had. We produced a bit of magic ourselves too, but of course, we had to defend and I think the players were magnificent in their work.