"It was a harsh scoreline but we were not good enough in our box and we weren't good enough in their box when we had the opportunities," Moyes said.
"Any small decisions did not go for us; the flow always went in Chelsea's favour tonight.
Wolves boss Nuno Espirito Santo to Amazon: "We were always in the game. We were well organised. In the second half we played really good football.
"In the first half the game was tight, Chelsea had the ball.
Lampard said it provided a dose of reality to those who say his side can win the league.
"It is a long season and these people talking about us winning the league with the best squad, it is ridiculous," he said.
Chelsea manager Frank Lampard: "I was nervous of Leeds. They're a threat until the end if you don't get a cushion.
"They are pretty unique in their style and they're well coached.
Newcastle manager: "I'm frustrated because we can't get a result," added Bruce, whose side have won once in five games. "I make no excuses but we've played three of the top six in the last few weeks.
Sheffield United manager Chris Wilder speaking to BBC: "I think at times my teams are naive. It's irrelevent. We have given away some poor goals. I think we have to look at ourselves.
Chelsea defender Ben Chilwell: "It was a tough match. We knew if we weren’t ready for a fight we’d get bullied. We came here ready for a fight and also played our style of football.
Chelsea boss Frank Lampard: "It went as I sort of expected. I thought we'd have a lot of possession. We created enough to win the game.
"The clean sheet factor against a side set up to counter-attack - that was excellent.
Manchester United manager Ole Gunnar Solskjaer on BBC Match of the Day: "It was an even game. After a slow start, we grew into the game and played some decent stuff.
"We missed the crowd behind the goal there to suck the ball into the goal, which happens so many times at this place.
Chelsea boss Frank Lampard, speaking to BBC Sport: "You go two goals up you want to finish it off. It was the best we've played this season for sure at this stage. But Southampton are a good side.
Chelsea manager Frank Lampard told BBC Sport: "There is a lot of reactionary stuff about us because of expectation. After West Brom people wanted to react. I don't and even after today I won't react too much, we are still working.
Chelsea manager Frank Lampard speaking to Sky Sports: "It is two points lost at the end of the day - and that's no disrespect to West Brom. You come here and you know the transition and any mistakes would be something they would jump on - that and set pieces.
Liverpool manager Jurgen Klopp speaking to BBC Sport: "It's always a tough game here. I liked the first half. It was two teams that wanted to play, create, defend and make things happen.