The former Chelsea boss was officially revealed as Jens Keller's replacement on Wednesday and is tasked with turning around the fortunes of a side that sits 11th in the German top flight with eight points from their first seven games.
Schalke have been Champions League regulars in recent years and the pressure will be on Di Matteo to ensure the Gelsenkirchen outfit's place in Europe's top-tier club competition despite their disappointing start to the campaign.
However, Di Matteo insists he has the experience to handle the pressure from Schalke's supporters.
"In over 100 years, nobody has ever been able to keep a lid on the fans here," he said. "When you think of Schalke, you think of the passion of their fans, of this big and ambitious club.
"I know the demands are high here, but I've been in the football business for 24 years.
"I've worked in Switzerland, Italy, England and now in Germany and I think I've got the experience needed to deal with it.
"The club wants to qualify for the Champions League automatically, and that is my aim too."
Di Matteo, who guided Chelsea to Champions League glory in 2012, believes an improvement in defence will be key to Schalke's hopes of success this term, although he is adamant his side will not be boring.
"The impression I have is one of a good team who have a lot of potential going forwards, but certainly have a few problems in defence," he added.
"They've had a lot of injuries too, but I think we've probably got to work on the defence a bit.
"In my opinion, you need a solid defence. Not just the back four, but the general organisation, and then you can build on that.
"If you look, you will see that my teams have always scored lots of goals.
"We'll try to play a successful game. You've got to find a balance in the team - solid at the back and have something going for you up front."
