- Stephan El Shaarawy (47')
- Nemanja Matic (83')
- Antonio Candreva (12')
- Boulaye Dia (54')
Roma could yet make the Champions League via an alternate route if they beat Sevilla in the Europa League final on May 31.
Asked about the latest Juventus verdict, Mourinho told DAZN: "This is a joke to me, learning this with two games left to play. Had they told me this before Monza (1-1), before Bologna (0-0), our approach would have been different.
"But knowing that Juve were taking points and that our best situation would have been to bet everything on the Europa League, we decided to do so."
Roma were without forward Paulo Dybala, who has yet to recover full fitness after he took a blow to the ankle away to Atalanta at the end of April.
"How is he? Bad," Mourinho said. "I don't know if he will recover for Sevilla."
Candreva's goal took Roma by surprise as Lassana Coulibaly's cross was put away first time by the midfielder.
Roma thought they had levelled in first-half stoppage time through Roger Ibanez, who bundled the ball past goalkeeper Guillermo Ochoa after a corner, but the effort was ruled out after a lengthy VAR review for handball in the build-up.
The hosts, however, did equalise two minutes into the second period after Ochoa saved Lorenzo Pellegrini's free kick and El Shaarawy was on hand to score.
Salernitana restored their lead in the 54th when Dia bundled the ball in from close range off a Krzysztof Piatek cross.
But Roma, now without a win in six consecutive league games, equalised once more through half-time substitute Matic following a corner seven minutes from time.
They next travel to Europa Conference League finalists Fiorentina, who are 11th, on Saturday before they end the season at home against lowly Spezia on June 4.
- Andrea Colombo