The Belgian winger insists he was disappointed that the Italian manager was dismissed but says he and his teammates must put that behind them and start again under Rafa Benitez
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.
Hazard says it is never easy to see a boss go, especially when that manager brought him to the club, but added that they must focus on getting on with their jobs.
"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.
He added, "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.
Di Matteo's firing is the first time that Hazard experienced a manager change and he admits at times he wonders if there was anything he could have done differently to save the Italian's job.
"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," Hazard remarked.
"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."