Chelsea begin their Premier League campaign on Sunday away at Wigan Athletic, with Di Matteo tasked with a significant improvement on sixth place last season.
"Expectation levels are always high. It might have added a little pressure but it was always so high anyway," the Italian told a news conference on Friday.
"It's an ambitious club and we know we have to try and win trophies and be successful."
Having been made interim manager in March with the team in turmoil following the sacking of Andre Villas-Boas, Di Matteo sparked a remarkable turnaround in the club's fortunes in the final two months of the campaign.
"All the players are looking forward to finally starting. Our aspiration is to do better than last season in the Premier League," he said.
"I still believe Manchester City is the favourite. They haven't lost any key players, but [Robin] van Persie is a good signing for [Manchester] United.
"We have to try and catch up with the Manchester teams. The gap last season was big so our aim is to catch them up."
Di Matteo added that his preparations for the new season had been disrupted by the European Championship and the Olympics, and that it would "take a bit of time" for Chelsea to hit top gear.
"Oscar has only been in the building for a day and a half, so we will see. I still have to think about it for Sunday, but there will be plenty of time to play," he said.
