Apart from the draw against Lecce, at least Roma has made great progress after De Rossi became coach of this team because they have only lost once so far, but Roma did waste the opportunity to keep their chances of sticking with Bologna to reach a position in the top four.
You can say that De Rossi helped Roma to play more attacking and beautiful football but to say he helped Roma make great progress in top four race, it is not true.
Mourinho and Roma were 5 points less than top four before Mourinho was sacked and De Rossi came. Now, after a draw with Lecce, Roma are 5 points less than a fourth position again. It's the same gap like months ago with Mourinho.
I do agree that Roma has a harder time now after this result, they should have won this game without a doubt. However, with the way it is looking right now, there are 8 more games, meaning 24 more points to collect, and Roma is only 5 points behind, in a situation they do better, they could take that fourth spot and they would deserve it as well.
If they had De Rossi since the start of the season then I would guess that they could have been fourth easily, or if Bologna didn't go on that amazing winning streak that nobody expected, Roma would have still be fourth. In any case, if they go to europa, that is still not a terrible deal and they could do well there as we have seen so far, I believe they will be able to do fine.