Jose Mourinho's side have won eight of their last nine games in all competitions and advanced to the Capital One Cup quarter-finals in midweek after a 2-0 success at Arsenal.
The Blues are also just two points behind their London rivals in the Premier League table and are also in a good position to qualify for the knock-out phase of the UEFA Champions League after winning two of their three group games.
Eto'o is aware of the difficulty of winning every competition and is adamant that Chelsea will not be over-confident in their pursuit of success.
"It's going to be difficult, yes," Eto'o told The Sun. "But we've got a good team and will not sacrifice our chances of winning one competition in preference for another.
"We're trying to win every competition and we will get there. We have as much chance as any rival.
"There's a lot of confidence in this group but we must stay focused. I realise each and every team can win. Until the referee blows that final whistle, even if you're winning 4-0, the other team is capable of coming back and even getting a fifth goal.
"We'll keep positive but still be a little suspicious as too much confidence can leave doors open for mistakes."
Eto'o, who has scored once in nine appearances since joining Chelsea from Anzhi Makhachkala before the transfer window closed, has been pleased with how he has adapted to being in England.
The Cameroonian added: "I've adapted to life here very well, even if I would have liked to be playing my best football much quicker.
"At my best I'll be able to bring something valuable to my team-mates, the club and the fans.
"It was really weird for a team like Chelsea, one of the best in the world, for all the strikers to not be scoring prolifically. But when I scored, it has set my mind free and now the other strikers too.
"Juan Mata did the work by scoring again against Arsenal on Tuesday and the team is winning, which is all that matters."