Everton boss Carlo Ancelotti: "Really pleased for the result, the first half was good, second half more difficult because Crystal Palace put a lot of pressure on us. We defended well but we could play better with the ball. It is good to see the spirit in the team in this moment. We have started the season well.
"We have to look only for the momentum, that is good in this moment. In a busy time with another game on Wednesday, we have to keep the motivation, ambition and we are doing really well. The danger is behind us all the time when we do not behave properly.
"I am not the right person to judge the decision of the referee. It is not only one referee that decides and we have to adapt to the new rules on the handball. It is difficult, but we cannot do nothing."
Everton skipper Seamus Coleman: "Very satisfying, Crystal Palace started the season strongly so it was a big game for both teams. We did not play that well but we knew we were up against a tough team and delighted to go back up the road with all three points.
"James Rodriguez is very exciting, from day one we could see the quality he has in training and he has brought that into games. A great lad but Abdoulaye Doucoure and Allan have been so important for us, the three new signings have been fantastic.
"Allan plays that role fantastic, Idrissa Gueye played it but now it gives us licence to get forward.
"Being a defender in this day and age is hard enough with wingers but then to be thinking about your hand in the box is tough.
"When I spoke to the lads, it is about day to day and being professional and not getting carried away with wins and not get too down with defeats. We want to be successful at this football club as you can see with the finances and the manager we have."
Everton striker Dominic Calvert-Lewin: "I thought it wasn't our best performance today but we stuck in there and got the result to keep the momentum going.
"It is early days but we are looking to build on every game, the more we are training together, it is exciting times but we are not getting carried away.
"The referee gave the penalty for us and it looked like it hit his hand. Richarlison put it away. the refs have tough job whether it is a penalty or not."
Crystal Palace defender Joel Ward speaking to BBC Match of the Day on the handball rule: "It is [confusing]. When you look at the motion and the momentum [of players], it's very hard to play with your arms behind your back. It is what it is, we have to dust ourselves down and go again. There will be conversations about [the penalty decision] I'm sure.
"Unfortunately it went against us, we can't dwell on that now. Let's not take away from the fact we have started well. We're making it hard for people to beat us, were limiting the amount of efforts and chances against us and from front to back we are well-drilled.
"So far it is going well for us. The restart was a strange period, as it was for all clubs, and at the start of the new season you have to forget what was and focus on what is."
Joel Ward added: "Much like our last two performances we were well organised and we made it difficult for them and nullified their threats for the majority of the game."
On being penalised for handball: "I think my thoughts will stay with myself, everyone else can talk about them but we will just get on with it. I'd rather keep my thoughts to myself.
On the new rules: "I think there are certainly some teething issues that need to be ironed out. They may need to look at how people move, the functionality of how people move. Some will go for you and some against you."