Everton manager Rafael Benitez tells BBC Match of the Day: "I think that we started the game quite well, we had a lot of situations on the counter in the first half and the final decision was not right.
Brentford manager Thomas Frank speaking to BBC Match of the Day: "Happy with most of the performance. We started the game brilliant at a difficult place to play. We were brave, pressed high and scored and I felt we were really on top of the game.
Aston Villa boss Dean Smith, speaking to BBC Sport: "We were unrecognisable from what I've seen in pre-season in the first half and what I had seen last season. We lacked intensity and got done on the counter.
Aston Villa boss Dean Smith: "I think the fans helped us over the line against a very good Chelsea team. The first 20 minutes I had to count there wasn't more than 11 of them as they seemed to get overloads all over the pitch.
"It's a big game for us [on Sunday], it's a big game for them [Leicester City]. We have to get over this. We will work tomorrow, there is no doubt we have to be ready and we know what we have to do," Tottenham interim boss Mason told BBC Sport.
"In the second half that was the Crystal Palace that I've seen in the last four years - that never-say-die spirit," said Hodgson.
"We accept we'll never roll teams over and we have to work hard to get a result and we did that today.
Aston Villa boss Dean Smith, speaking to Sky Sports: "I thought we controlled the ball well in the first half without creating chances. The second half was a bit scrappy. It started as a basketball game but we never took the control we wanted.
Manchester United boss Ole Gunnar Solskjaer to BBC Sport: "A great result and it takes a little bit of pressure away from having to get results because the next two [versus Leicester and Liverpool] are against very good teams.
"We lost a big opportunity to stay in the fight," Ancelotti told BBC Sport. "We're still in the fight but with less possibility and more difficulties.
"We didn't start the game as well as this kind of game demands.
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.
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.
"If you make mistakes like we did for their goals and don't create or show much quality in the final third, you are going to lose games," Villa boss Smith told BBC Sport.
"They got numbers behind the ball but we got into the box a number of times and either hit the first man or didn't show the quality needed.
Sheffield United boss Chris Wilder: "We've not got enough results in these kind of tight games. My team has shown tonight that the majority of the time, if not all the time, they give everything to get a result.