Roma will face six-time champion Sevilla, which knocked out Juventus with a 2-1 win after extra time to prevent an all-Italian final.
The final takes place on May 31 in the Hungarian capital of Budapest.
Leverkusen forward Moussa Diaby hit the crossbar early and Roma goalkeeper Rui Patrício was busy at times but Roma’s defense held firm, despite the team rarely venturing forward and managing just one effort on goal in the entire game.
Mourinho is bidding for back-to-back European titles with Roma after winning the inaugural edition of the Europa Conference League last season. He has won the Europa League — or UEFA Cup as it was previously known — with both Porto and Manchester United and also has two Champions League titles.
“It’s an unbelievable team, I don’t know if I can ask for more from Roma but these guys deserve something special,” Mourinho told Sky Sports.
Winning the Europa League could also be the only chance for Roma to qualify for next season’s Champions League.
Sevilla trailed 1-0 at home in the second half but substitute Erik Lamela set up the equalizer that forced extra time and then headed in the winner in the 95th minute at the Ramón Sánchez-Pizjuán stadium.
After the two teams drew 1-1 in Torino last week, substitute striker Dušan Vlahović gave Juventus the lead in the 65th with a precise chip from inside the area.