Chelsea remain nine points adrift of runaway leaders Manchester City despite the win, but Cahill warned that there is still a long way to go in the Premier League title race.
"I have to admit it was a superb performance from us, every single player, and collectively we are very happy," Cahill told Chelsea's official website.
"I felt we played some good football, we kept the ball when we needed to and scored goals. We saw a bit of everything from us, so performance-wise it was very, very good.
"[Man City] have started started off full steam ahead and that's great for them, but we're not even at Christmas yet, so let's just hold fire and see how they get on.
"They look fantastic at the moment and we have taken a fair bit of criticism at times this season, but we've had three clean sheets on the bounce in the league now, it was a great performance and we've still got a long way to go."
Chelsea take on Qarabag in the Champions League on Wednesday before facing Liverpool next weekend.