The Blues are currently second in the table with 23 points from 10 matches, one point behind leaders Manchester United.
"We've got new lads, like me, who have not been scarred by that history [of slipping up after a good start]," he told The Guardian. "And I don't think anyone could argue we don't have a squad capable of winning the Premier League.
"When we set out in the summer, we wanted to improve on our league position. Sixth wasn't good enough.
"We weren't where we wanted to be when I came in last January and, at the end of the season, we weren't where the lads expected to be. So we needed to improve and our start suggests we are."
Cahill added that a mixture of youth and experience in their squad will be useful for Chelsea against their title rivals this season.
"We've got a blend - the class and experience of some of the older guys, and younger lads who are established already," said the 26-year-old.
"These are exciting times but the expectation level is still massive. I've had an amazing time here so far but I'm hungry for more. We all want to push on."
Chelsea will host Liverpool at Stamford Bridge on Sunday.