De Rossi was sacked and replaced by Ivan Juric by Roma on Wednesday.
Nainggolan told Il Tempo: "My first reaction when I read the press release about De Rossi's dismissal? It seemed like pure madness. Last year he came to Rome saying he wasn't even interested in the money, then he earned his confirmation with good results.
"They gave him a three-year contract announcing it with great fanfare and now this...
"After four games he was fired, it seemed strange to me, pure madness. They can say what they want about the results, but if all the players are on his side, evidently there is something more than what they say.
"This dismissal seems like a joke to me, it cannot be justified by the fact that he has drawn three times in four games, in the end he has only lost one game."
On Juric, Nainggolan continued: "He did well with Torino and Verona. Now he's in a big team, he has to bring out the players' qualities a bit more. He's always played very physical and very intense football. Roma doesn't have a team to get into the top four. It won't be easy at all to get into the Champions League."