Neto struck late to earn the 2-1 win - after the Cottagers had gone ahead through Alex Iwobi. Tyrique George hit Chelsea's equaliser before Neto's winner on 93 minutes.
Neto said afterwards, "I think it could be a big part of the season for us. We showed character. To be honest, I have no words.
"It is not easy to spend all season in the top four and we were out before this game. The character the team showed, we now need to think about Everton.
"When I received the ball, I just span around and shot as hard as I can. The ball went in. The first one, Leno did an unbelievable save and I was so frustrated that the second one I had to put all the power into the shot.
Fans so important
"The fans don't have the notion of the part they do for the club. Today at the end is what we need from them. They play a big part for the team. On the pitch, we understand that sometimes they are upset with us. But with them we are stronger."
On George's goal, Neto added: "What a finish it was. He has been working with us for a while. Today he showed what he can do, he scored a beautiful goal and we go from that.
"The belief has always been there, even in the bad moments. Sometimes in this game it is not about the quality, it's about the spirit and that's what we showed today - and I think we deserved to win."