The Italian manager won the FA Cup and Champions League double last season, but was sacked following a poor run of form that culminated in a 3-0 loss to Juventus.
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"Look, I knew before I came here where I was 'putting my feet' and the sort of club I was coming to," Hazard told the Independent. "I knew that Chelsea was a club that changed its manager reasonably often.
"Obviously I didn't intend it to be that quick because Di Matteo was the person who signed me and I was looking forward to a relationship and working with him for some time. But I don't have any regrets.
"We have a new manager now and again it is about stressing we must try to get as high as we can up the table, go as far as we can in the cups, play well and win as many trophies as we can.
"I think it's the first time it has happened to me in my career when a manager has gone. It's never easy. It's something that is part of football life. We have to put our disappointment to one side. Although I was sorry because he was the manager who signed me.
"Again it goes back to it being part of the football life. It is natural. You question yourself all the time as a footballer. You have to focus on the positives. It's the manager who picks the side but it is the players who are out on the field, so in a way he depends on us a little bit.
"You think 'Oh if that chance had gone in, or if I had not scuffed that shot, he might have still been in a job'. So you do feel that responsibility but you have to check yourself and say 'This is football'. And it is a case of starting from zero and getting on with things."