The Blues failed to stick with the leaders under Andre Villas-Boas and, even after Roberto Di Matteo took charge, Premier League results failed to improve as the club finished sixth, 25 points behind champions Manchester City.
However, after adding the likes of Eden Hazard and Marko Marin to the squad over the summer, Cahill feels Chelsea are capable of being among the title contenders again.
"The most important thing is to improve upon that," Cahill told Sky Sports News.
"When you look at the previous however many years, they were always finishing first or second.
"I'm pretty new to the set-up 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 are currently in the United States for a pre-season tour and Cahill is looking forward to playing alongside John Terry again after the captain was given extra time off before flying to New York.
Cahill added: "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.
"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."