Mourinho suffered his first loss in seven European finals when Sevilla defeated the Italian side on penalties after a 1-1 draw in normal time.
However, it was an ill-tempered affair on both sides, with Taylor brandishing a total of 14 yellow cards -- a record for a Europa League match.
After the match, a video shows Mourinho swearing at the Premier League referee in the car park and calling him a "f--king disgrace."
The Portuguese coach fumed at Taylor in his postmatch news conference for not awarding a penalty kick to Roma for a perceived handball during the second half -- as well as a number of other decisions he thought the referee mishandled.
"The referee seemed like he was Spanish," Mourinho said. "The result was not fair, and there are a lot of instances to reexamine."
Mourinho added: "This is a European final, and with this kind of refereeing, it is hard to accept. If we talk about refereeing situations, it's not two or three: it is many, quite apart from the big decisions. Those of us who have been in football a long time realise immediately what is going on.
"[Lorenzo] Pellegrini falls in box and given a yellow card; [Lucas] Ocampos did exactly the same thing and he doesn't get one. It's a scandal. VAR called the referee and shames Ocampos, but there's no card given.
"[Erik] Lamela -- who, by the way, scored one of the penalties -- deserved a second yellow but didn't get it. And let's not even talk about the big decisions. That's just the small details."
Having also received a yellow card during the match, Mourinho could be hit with a multi-match ban from future European games by UEFA.
After receiving his runners-up medal on the pitch, Mourinho walked toward the stands and handed it to a young fan in the front row, and later said: "I only keep the gold ones."
Sixth-placed Roma face relegation-threatened Spezia in the final round of Serie A on Sunday, one point behind Atalanta and one point ahead of Juventus. Fifth place qualifies for the Europa League spot and sixth place for the Conference League.
Information from The Associated Press was included in this report.