Those performances of Roma doesn't help De Rossi to get a long contract at Roma. It seemed Roma failed to perform their best when they were under pressure. The high target of finishing top four may be a factor of this bad form. This result will put De Rossi under evaluation of his worth to continue his role at Roma next season.
There is suggestion that Roma has given up early due to their small chance to achieve their target. The consistency of their competitors like Atalanta and Bologna made it hard for them. The failure in Europa League shouldn't a reason for this decreasing form as they were lost to a better team whose have a great season. The desperation of unable to get the target is the only explanation.
I think De Rossi will continue to be retained by Roma and next season of course the target that must be achieved is of course finishing in the top 4.
This season De Rossi took over Roma at the end of the season so he only had relatively little time to change Roma performance. Roma also has to improve their efforts to bring in new players to be able to compete with AC Milan or Inter Milan. This season, Roma failure was very disappointing because fans hoped that Roma could return to playing in the Champions League, but that hope was lost because Roma lost a lot of points.
De Rossi has good tactics in building a squad but he needs quality players to be able to bring Roma to compete at the top. Lukaku has also performed well this season and I think Lukaku just needs the right duel to be able to bring new changes to Roma front line. Apart from that, Roma also failed in the European league this season, which is of course a special concern for management to evaluate the squad by recruiting new players in the transfer market.