Actually when Daniele De Rossi became Roma's manager he was initially doing well for the club of which most football analyst were applauding his managerial experience than that of Jose Mourinho
De Rossi helped Roma to play more attacking, show more beauty football that matches with Roma's traditional style but in football, club need titles, not impressive performances without titles. I agree that De Rossi as a young coach, already shown his ability very well with Roma. If he can do better, Roma will have good chance to win titles with him and with good transfer budget spent in this summer, De Rossi will have a better team for a new season.
Jose Mourinho was doing bad for Roma as at the time Daniele De Rossi was hired and the club's management just feel they are paying Jose Mourinho too high when they can't even get to the Champions League
AS Roma actually did not have too bad result when they decided to fire Jose. It's just Jose gone through a tourmalet with many big matches with not good results. De Rossi got a long honey moon with Roma against non big teams but in late of season, when Roma played against big teams in Serie A, we saw what happened.
At the end, Roma ended Serie A without a good position to go to Champions League, it's nothing better than what Jose did.