The 42-year-old was initially appointed as Andre Villas-Boas' successor on a temporary basis but went on to lead the Blues to victory in the FA Cup and Champions League.
Despite the Italian's stunning success, Chelsea owner Roman Abramovich was reportedly interested in other candidates such as Guardiola, who stepped down at Camp Nou after four seasons in charge this summer.
"I don't feel any shadow above me or behind me," Di Matteo told reporters. "There has been speculation about other managers since day one and I have always lived with it pretty well.
"Everyone can say what they want. I will just focus on my job and try to do the best I can. I'm pretty happy with my new contract and that's why I signed it.
"But I have been in football all my life and I understand how this business works. I clearly know that managers are judged by results. It's no different for me than anyone else. The pressure is always there.
"Chelsea are always looking to win things and last season was not easy even if the end of the campaign was a pretty fantastic time. I understand why it took a bit of time for the club to come to their decision and I respect the way everything has been handled."
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The Italian also revealed that he had fielded enquiries from other clubs while waiting for the west London side to make their move.
"It wasn't a case of not talking to me for four weeks," he continued. "We were always in touch and there was contact from other clubs. I was actually pretty relaxed about the whole thing.
"There was no time limit on it because it was an important decision for the club and I have no problems with that at all. There were never any doubts for me and I'm very happy to be here.
"Now I'm looking forward to working with this group of players and bringing more success to the club."