De Rossi replaced Mourinho on Tuesday, with Roma ninth in the league after their 3-1 loss to AC Milan, but the Portuguese manager still has the support of the fans and banners have appeared in recent days protesting about his sacking.
"Nobody will ever cancel the love the fans felt for Mourinho but nothing prevents them from loving me too, and continuing to support the team at the stadium," De Rossi told a press conference on Friday.
As a former, much-loved Roma player, De Rossi is under no illusions as to why he was chosen as the man to bridge the gap with the fans after Mourinho's dismissal.
"It was a well thought-out choice because if you dismiss a much-loved coach you have to take into account several factors; with someone else, the reaction of the fans could have been worse," De Rossi said.
"I'm not stupid, it's obvious that if I'm here, it's not because they were struck by the football played during my time at SPAL."
De Rossi had his first taste of management at SPAL last season but the experience lasted just four months as three wins in 16 league games left the club in the Serie B relegation zone.
His contract with Roma expires at the end of this season but De Rossi had no doubts about returning to the club where he spent 18 seasons as a player.
"The owners have been very clear about the duration and tenor of my stay here," De Rossi said.
"I asked for a bonus if we qualify for the Champions League but I would have signed anything; it seemed to me a necessary gesture considering my history here."
Luckily, as a Roma fan, De Rossi has already been keeping a close eye on the team and despite their position in the league, he is hopeful that a Champions League place can still be achieved.
"I'd be happy if we were in the top four at the end of the season; it's not an easy goal but it's absolutely possible.
"If you change a coach it's clear that there are problems; I'm starting from scratch. Fortunately, for reasons of support, I have seen all the games, so I know the team well and I have shortened the study period a bit."
De Rossi's first test comes on Saturday with a home game against struggling Hellas Verona, currently 18th in the Serie A standings.
