Most importantly, he hasn't even seen the winter transfer break yet, lets see what he is willing to do or even Roma is willing to do. If they can get some good players then we could see them get better. At the very worst case scenario, they will just stay at Serie A, not going to relegate and they are not going to end up with any European competition next season and just try again all over.
After spending a lot of money, which they refused to give Jose Mourinho in his two and a half season, I believe that Roma will not spend considerable budget for player transfers in the winter transfer market. If they can loan some players, they will do it, but purchasing new players sounds impossible.
Ranieri will have to make all of his plans to improve Roma and rescue them with players he has now.
I think they have just followed a trend with Mourinho. Everyone knows that he is not the best coach when he is coaching the club for the third year consecutively. And I think as soon as they saw him bringing in bad results, they thought it was not going to be good for them to keep him any longer. But what was really disappointing is that if you change a coach, you generally look to bring a coach who is actually better. But it almost looked like they were bringing in a coach who was actually a downgrade. The decision did not make sense to me. And the decision of sacking Mourinho did not make sense to me in the first place and of course, now they are suffering.