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.
A 2-2 draw between Newcastle United and Tottenham Hotspur was not the result Fulham boss Scott Parker or West Brom gaffer Sam Allardyce would have hoped for last Sunday afternoon. But for the Newcastle faithful, it was a sign that they could yet stay in the Premier League.
The English Premier League is one of the most cut-throat soccer competitions in the world and this is great news. After all, we all love to see a fairly competitive game of soccer and when this is the case, we can't deny the beauty of the game.
Drawing Atalanta in the Champions League was one of those ties that had the potential to go horribly wrong for Real Madrid. The Italian side are a difficult team to predict – at one moment they can look like world beaters while the next they resemble a bunch of amateurs.
The weekend continues with the Liverpool's worst ever home top flight form with defeat to Fulham, while Manchester United puts a stop to Manchester City's 21-match winning streak.
While Fulham's win at the Anfield moves them a step an inch from the relegation drop-zone, Newcastle United slip into the relegation fight and Brighton & Hove Albion's bad luck goes on.
Manchester United have reportedly contacted Leeds United over the possibility of signing Raphinha, who is also a target for Liverpool.
According to a report by Brazilian outlet UOL Esporte, Manchester United have stepped up their efforts to sign Raphinha in the summer transfer window.
Manchester City have been handed an encouraging boost in their planned pursuit of Borussia Dortmund's star striker, Erling Haaland, with details emerging as to where the power may lie in the Norwegian's team of representatives.
Premier League club Arsenal F.C are reportedly keen on completing a summer move for Jordan Amavi, who is yet to agree a deal with his club Olympique Marseille, who has five points adrift Europa League group stage qualification.
The British Government have reportedly contacted UEFA about the opportunity to host the whole of the upcoming European Championship’s in England.
According to recent newspaper reports, culture secretary Oliver Dowden has told UEFA that the current vaccination scheme in the UK will be advanced enough by the summer to allow fans to attend football matches before the rest of Europe.
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Manchester United have been linked with Raphael Varane for a very long time and the latest reports suggest that the Red Devils could move to secure his signing in the summer.
The 27-year-old central defender’s contract at the Bernabeu will expire in 2022 and Marca claim that Real Madrid would consider selling him if he does not agree a new contract.
Manchester City have reportedly set their sights on former Liverpool striker Danny Ings over a possible move in the summer.
According to a report by The Athletic, Manchester City are set to enter the transfer market for at least one striker in the summer transfer window amid uncertainty surrounding the future of Sergio Aguero and Gabriel Jesus.