The Blues have enjoyed an impressive season under Enzo Maresca so far but are ignoring outside talk suggesting that they could challenge for the league title.
Sancho told Sky Sports: "We are taking it game by game and every game is going to be tough. We've got a long season ahead so none of the boys are overthinking anything right now. That's what all the guys are saying to each other.
"We haven't done anything yet but we're grateful to be in this position. We're training hard and putting in the shift on game days."
The winger joined Chelsea on loan from Manchester United this summer and feels lucky to be playing for the club he supported as a child.
Sancho said: "I grew up as a Chelsea fan. Didier Drogba and Frank Lampard were the players I looked up to when I was growing up so it's a nice feeling.
"I feel like me making it professional alone is the best feeling. Any young kid can dream of just being out there and playing football so I'm truly blessed in that respect."
Sancho has scored in consecutive Premier League games for the Blues and is looking to prove himself in the competition following an unfulfilled spell at United.
Asked for his aims for the rest of the season, the England international said: "Hopefully I can carry on creating opportunities to score and assist for my teammates and just get a good rhythm throughout the season.
"It's difficult playing in the Premier League and having other competitions. It can become overwhelming sometimes because there's a lot of games back-to-back.
"I feel like the coach gets the instructions across and he makes sure we know what we're doing on the pitch and how we help each other so I think it's good."