The Ivorian striker scored the winning penalty in the Champions League final victory over Bayern Munich in his last game for the west London club, before moving on to Chinese outfit Shanghai Shenhua.
The Blues' boss paid tribute to the 34-year-old's career in west London but indicated that he is looking for players already at the club to step up and fill the striker's role.
"We have a lot of quality players," the Italian told reporters. "Didier Drogba has been superb for the club for many years. People will rise to the occasion to fill the role he left. We have [Fernando] Torres, Daniel Sturridge, [Romelu] Lukaku. We have options.
Fernando Torres picked up the Golden Boot award at Euro 2012 and Di Matteo is now looking for the Spaniard to carry on his form on his return.
"He was fantastic," the Italian added. "What the Spain players achieved in the last few years is amazing. It will bring confidence, sportsmen need confidence to do well and hopefully they will come back in good form."
Chelsea have already brought in Eden Hazard from Lille this summer, and Di Matteo insisted that the Blues will not rush into the transfer market for additional players.
He continued: "Hazard wasn't cheap so we have already spent some money. It's not just about spending money though, it's about bringing in quality players.
|8/1||Fernando Torres is 8/1 to be the 2012-13 Premier League top scorer with William Hill|
The ex-Blues player became permanent manager over the summer and despite rumours of Pep Guardiola taking over, even with Di Matteo given a contract, the Italian is determined to bring success to Stamford Bridge.
"I'm very happy to be here, it's a fantastic club to work with," he stressed. "I always said I would respect the club's decision. I'm looking forward to meeting with the players and hopefully bringing success to the club.
"We were always in contact, it was just a matter of time. We needed a holiday. There was contact from clubs too, but this is normal.
"I've been in football a long time, I know managers are judged on results, I'm no different. I just focus on my job to do the best I can."
"There has been speculation from day one. I've lived with it, I don't feel his shadow."
Frank Lampard missed England's Euro 2012 with injury but Di Matteo is confident he will be fully fit for the new campaign: "Frank should be okay for the start of the season, it was a shame he missed the Euros.
Doubts also remain over the future of a number of Chelsea players but Di Matteo confirmed Yossi Benayoun and Florent Malouda will be with the club this summer.
"They're going to come back in and I'm looking forward to seeing what they can do in pre-season," he said.