Roma will not complete this season with a high rank enough to participate in Champions League next season.
No, there is no chance to finish in UCL zone if Atalanta can win 1 more match. Next match, Atalanta will play against Torino at Atalanta own stadium. It is very unlikely that Torino will beat Atalanta, I assume this will be another 3 points for Atalanta. It means Atalanta will be safe to finish in 5th place at the end of the season.
It is a task that was not achieved by Mourinho with his two completed seasons in Rome but De Rossi will not achieve anything better than Mourinho.
If simply look at result, De Rossi did worse than Mourinho, no Europa League final match (worse) and no Champions League spot (the same).
We can't judge De Rossi did a worse thing, it is his first season. It is not too bad to finish in Europa league zone in Serie A. I think De Rossi needs time to adapt with the the whole players, he also needs time to build the team with his own way. I believe De Rossi will ask for buying some new players that he think to be helpful for AS Roma. AS Roma needs to improve the quality of their squad if they want to finish in a better position in the next season. The defense and attacking line should be improved, AS Roma only have quite good players in midfield line.
They are very important attacking players in Roma and without either Lukaku or Dybala, Roma will have big problems in attacking. Baldanzi was bought as Roma's preparation to separate with Dybala but this young player did not play too well so far.
Lukaku is just a loan player from Chelsea, Dybala often gets injured. AS Roma actually can't rely on these players. They only have Tammy Abraham but this player no longer performed well after he got injured for a long time. They need new players in the attacking line.