Manchester United manager Ole Gunnar Solskjaer speaking to Match of the Day: "We should have scored many more goals.
"It was an excellent performance from the lads, when you see them going forward it is a joy to watch.
Brighton manager Graham Potter: "It's pleasing to get three points against a team that carry a threat."We had to be disciplined and we were.
"We needed patience and understanding playing against side that carries a threat.
Everton boss Marco Silva, speaking to BBC Match of the Day: "If VAR saw something in our box, why didn't it see 15 minutes earlier the penalty for Richarlison.
"Because of that my players are in the dressing room and don't understand.
"It was a captain's performance," said Villa manager Dean Smith.
"For the other side of the game people don't see, Jack ran 60 yards to back dispossess players [at times]. He was integral to everything, he got the goal and provided an assist.
Brighton manager Graham Potter: "Overall I was really, really happy with the performance. Great personality on the pitch, we attacked well, defended well.
"When we made mistakes we recovered, we created chances and played on the front foot as much as we could.
Chelsea "needed the win" over Brighton, said boss Frank Lampard after his first home victory as a Premier League manager.
"We haven't had a 90-minute game where we've controlled it enough [before now]," Lampard told BBC Sport.
Premier League strugglers Newcastle and Brighton played out a largely forgettable draw which does neither side many favours.
Brighton manager Graham Potter: "I'm a bit frustrated. I thought our performance was really good.
Substitute Jeff Hendrick fired in a stoppage-time equaliser to earn Burnley a point and deny Brighton their first home victory since 2 March.
The Seagulls were set to win it when Neal Maupay volleyed in Solly March's cross at the start of the second half.
Sergio Aguero was labelled a "special talent" by Manchester City boss Pep Guardiola after the Argentine hit two goals against Brighton, continuing his record of scoring in all four of his team's Premier League games this season
"Of course we need his goals, everybody knows it.
Brighton manager Graham Potter said he "can't defend" Florin Andone's challenge which resulted in the Romanian's dismissal in the Seagulls' 2-0 defeat to Southampton.
"It didn't look like a great tackle," Potter told Match of the Day.
Arsenal draw with Brighton to leave Europa League victory as only real hope of Champions League qualification
"We knew it was going to be difficult but our focus is now the Europa League," Emery, who won the competition three times in a row with Sevilla, told BBC Sport.
The big match between Chelsea and Liverpool ending in another draw, not really moving either teams forward from their current position in league standings.
Playing at Anfield, Antonio Conte's men were setting up a counter attacking system as they defended well and push forward in such direct fashion, creating several problems for The Reds' defense.
Chelsea Shocked, Liverpool Held While Man City Victorious in Premier League Opener
Three different results were earned by top Premier League teams in their opening fixture this Saturday as defending champions, Chelsea fell into a 3-2 defeat while Liverpool held in a thrilling draw and Manchester City got themselves all three points.