The Senegal international scored a late winner to lift Jurgen Klopp’s side back into second in the table, six points behind Chelsea after 17 matches.
Mane does not want to become distracted by hoping that Antonio Conte’s in-form side will suffer a dip, but he is confident Liverpool have shown they are up for the fight.
“I think wins like this show we’ll be there, yes,” he said.
“We are focusing on our team. It was important to get the three points at Everton. It is still early to talk about what is going to happen and we are thinking about ourselves, not Chelsea.
“But one of our ambitions is to go far as possible and we are going to try and do that.
“It was a very important goal and very important to win. The performance of the team was great – it was a different type of win from us and that is good.
“It was a derby and everybody knows how these games are, so the most important thing was not how we played, but to have the win. We got it and we are going to keep going now.”