Manchester City boss Pep Guardiola told BBC Match of the Day: "We did not create enough for the forwards. It is part of the game.
"In the last 10 minutes they had other chances, they are fast and can do it.
Liverpool matchwinner Trent Alexander-Arnold does not have to "prove anything", said boss Jurgen Klopp who wanted to focus on their "massive" 2-1 win over Aston Villa.
Alexander-Arnold, left out of the recent England squad, scored in the last minute as the Reds ended a six-game losing run at Anfield.
"We know they are a good side, everybody knows that, but we can't afford to play the way we did in the first half," said Hodgson.
"Both of the first two goals came about through balls lost near our own goal.
West Ham's Mark Noble : "The boys stuck in and dug in, we’ve lost Michail [Antonio] after 30-odd minutes after he was fantastic for us, and with Dec [Rice] missing out for us – that was terrible news and we hope he is back soon.
Everton midfielder Tom Davies: "We're really disappointed. We had chances to kill the game. It is poor from us. We need to be better. It starts after we score. We shouldn't be hanging on to 1-0 into last 10 minutes.
Manchester United boss Ole Gunnar Solskjaer told BBC Sport: "It's always difficult to play Brighton. We have had good results and we've had to earn them the hard way - we managed to find a way in the second half.
Aston Villa boss Dean Smith: "It's a big win - a win full of character in the end. We believe we've got a quality squad.
"It was certainly a very good last 20 minutes or so. Sometimes you need players to make an impact from the bench and the three who came on certainly did that and lifted our performance.
Wolves striker Fabio Silva, speaking to Sky Sports: "The team fight until the end. We have to be proud for that. In the first half we need to be more focused. The team need to move on to the next game.
West Ham's Mark Noble speaking to BBC Radio 5 Live: "The boys stuck in and dug in, we’ve lost Michail [Antonio] after 30-odd minutes after he was fantastic for us, and with Dec [Rice] missing out for us – that was terrible news and we hope he is back soon.
Newcastle manager Steve Bruce told BBC Sport: "I was delighted with the performance. I think we needed that. We needed to show what we're about. We had an awful five minutes where we gave an awful goal then they produced a good bit of quality to open us up.
Southampton manager Ralph Hasenhuttl: "When you see five goals in one game it's always good for television - not so good for the hearts of the managers.
"They don't normally give you a lot of chances but our game in the final third was fantastic.
Leeds head coach Marcelo Bielsa: "We think we managed to dominate large parts of the game. We had chances to score more goals and there were a lot of dangerous actions that didn't finish in shots that would have increased the number of chances we had.