The Cameroon striker, who moved to Stamford Bridge from Anzhi Makhachkala in August, doubled his tally of Premier League goals last weekend with a match-winning hat-trick against Manchester United.
Chelsea's 3-1 victory over the reigning English champions kept Jose Mourinho's men hot on the heels of league leaders Arsenal.
And with Chelsea also still competing in the UEFA Champions League and FA Cup, Eto'o is hopeful of tasting success come the end of the campaign.
"At the moment we are still in practically all the competitions," the 32-year-old told Chelsea's official website.
"If Chelsea are not the best club in the world then they are one of the best clubs in the world, so I don't know if we are going to win everything but the season is going well so far.
"The season is long, and there are a lot of things that could happen, but I hope to score more goals, help my team and then hopefully the season will end well for Chelsea."
Eto'o was delighted with his impact in Sunday's 3-1 win over United.
"I love the big games," added the former Barcelona and Inter forward.
"Before the game I spoke with Jose and I told him I wanted to play this game, but it's tough when we have other great strikers like Fernando (Torres) and Demba (Ba).
"It was good to get the opportunity to play and try and help the team win.
"The first goal took a deflection; the other two were good because I hadn't had much of the ball so I was glad when the opportunities came my way.
"It was a real collective effort and to take the three points was the most important thing.
"There is a huge difference between English football and the other championships, you almost can't compare it, but I am trying to adapt very quickly and that's okay."
