Roberto Di Matteo led the Blues to a Champions League and FA Cup double in 2011-12 but it took its toll on its performances domestically, as it missed out on the top four places let alone challenging the two Manchester clubs for the title.
Cahill, though, feels that the Blues are in a better position to push for domestic glory this season, particularly after acquiring the services of Lille superstar Eden Hazard and Marko Marin from Werder Bremen in the close season.
The 26-year-old told Sky Sports News: "The most important thing is to improve upon that [sixth-placed finish].
"When you look at the previous however many years, [Chelsea] were always finishing first or second.
"I'm pretty new to the setup here, but we're definitely going to look to improve as we should be. The squad we've got here is fantastic. Obviously, with the new faces coming in, we are definitely looking to improve and push for the league."
Chelsea is currently on a preseason tour of USA and Cahill is excited at the prospect of linking up with his club and international central defensive partner John Terry again when he joins up with the rest of the squad.
The club captain has been given extra time off due to his England duties and his recent trial, but the ex-Bolton man is champing at the bit to renew their partnership.
"He's huge for this football club. He's a huge player and it's good to have him back. We're gradually getting the squad back together," Cahill explained.
"When you think of Chelsea, you think of John Terry. We're looking forward to getting him back and getting involved in the next three games."