I agree that De Rossi could not improve AS Roma much because he did not have enough money. He made little progress but it is worrying that they have not signed many new players. Team might not be good enough to compete with best teams just with their current players. AS Roma needs to buy new players to do well in next season. Now that Lukaku has gone back to Chelsea they really need to sign someone new. Let's hope they announce some new signings soon to make their team stronger and compete better. Until then it is hard to see them doing very well.
Signing of new players does involves money and just like you have stated earlier, it appears like much .Oney isn't given to Rossi just yet so he's very likely to not be able to sign players just yet, the transfer windows are still open so they still got some time and let's hope that soon that will be able to get the funds needed to get players if necessary but if Rossi thinks he can better build on the players they have got already, then it's a very good one and will even be of advantage to the team by helping them save some funds well enough for the season.
Lukaku has left a space they really need to fill up in their team this season, he's role was a Viral one for them and now that he's gone they are sure going to need the replacement for him and make sure the team is able to still maintain some good strength that will be very useful to them for the rest of the season as they need to be consistent and continually improve in order to give the kind of performance expected just they did in the later part of the season which made us see Rossi to be good enough for the team.