This game is hard for Roma and Mourinho as there is no inner joy that is carrying them in this game. Playing shortly after having lost such an important final and the chance to qualify for the Champions League can be harder as it seems at first glance against a team like Spezia. By the way Spezia is fighting to stay in Serie A and this means they are not giving up and giving away any point whatsoever for free. They will try everything to at least win a point to make it less likely that Verona can overtake them when they win a point against Milan and Milan is already safe, which means that Verona has a chance to get a point.
In this case what you said is true because of course this is a mental match too because of course the spirit is a little fragile when something like this happens where they lose in the final and have to let the opportunity go, but still this has to go on because the season can't wait. if indeed they are late then of course apart from the Champions League, the Europa League zone will also leave so in this case even if they don't get the Champions League they should at least get the Europa League.
Spezia will definitely go all out in this match regardless they don't want to lose either because as you said this is also decisive for them.
It would be a bad goodbye from Mourinho if they now fail to qualify for the Europa League. I know there are rumors all day long about transfer activities and where the coaches go next and so on, but there are some links from Mourinho to PSG and he refuses to confirm to stay for another year in Rome. I think that is ok if he denies that, but now he as a coach should do as much as he can to one more time motivate his team and try to make this qualification come true. The scenario where they first lose the final and the Champions League qualification along with it and then also miss the Europa League qualification would be the absolute worst case for all of them, but Mourinho wouldn't really have to care if he knows that he will go to PSG.