The Italian was installed as caretaker manager at Stamford Bridge earlier this month following Villas-Boas's dismissal.
The Portuguese was widely rumoured to have lost the support of the senior figures in the Chelsea setup.
Di Matteo admitted to friction at the club, but insisted he had always supported Villas-Boas.
"He is a great manager and a great person and I will always respect him a lot," he told Eurosport-Yahoo!.
"But I did not hesitate when I was offered this chance. I deserve my new role. How can you hesitate when you have the opportunity to manage one of the most important football clubs in the world?
"All new managers inevitably replace a colleague when things go wrong or results are not up to expectations. This is the nature of football.
"I did my best and Andre knows it. I did not conspire against him and all the decisions we took, we took together. I have always behaved with the utmost professionalism and loyalty towards the club, the staff, the team and fans."
Since taking charge, Di Matteo has led the Blues to the FA Cup semi-finals and the last eight of the Champions League.
The 41-year-old insists reports of deep dissention in the Chelsea ranks are wide of the mark, saying conflict occurs at every club.
"I have never known a dressing room or a group of players which is easy for a manager to control," Di Matteo said.
"Of course there are strong personalities that occasionally collide with each other during the course of a season. But even in the media, do you never have problems with your colleagues or your editors?
"This is a normal work environment at a football club where there is an obligation to win and to always give the best of yourself as an individual and a group. Here at Chelsea we only have top-level footballers and great professional players.
"It is obvious that it is sometimes a challenge to keep so many top players in the same side happy. Everybody wants to play every game and everyone always wants to win but there is no problem with this dressing room."
Chelsea face Manchester City at the Etihad Stadium on Wednesday night. A victory in Manchester and an Arsenal defeat at Everton in midweek could see the Blues leapfrog the Gunners into fourth place.
And Di Matteo concedes a top-four finish is absolutely vital despite the team's recent progress in the domestic and European cup competitions.
"Of course it would be bad, really bad, if we do not finish in the top four," he said.
"But I do not even think of such an eventuality. We are Chelsea, we have great players and we will do our best to achieve what, for a club like this, is the minimum goal for the season.
"Entering the top four in the league and returning to the Champions League is our target. Everyone at the club feels this responsibility and we will do our best to succeed."