The defeat meant Roma failed to qualify for next season's Champions League and prompted questions about whether the 60-year-old would remain in the Italian capital, having been linked with Paris Saint-Germain.
"I have to fight for these lads and therefore not say objectively that I will remain," Mourinho, whose side was tied 1-1 with Sevilla after extra time, told Sky Sports Italia. "I spoke to the club in December when I had that approach from the Portuguese national team.
"I have not had any contact with anyone else since then. I have a year left on my contract and this is the situation."
It was Mourinho's first defeat in a European final, but he said he was proud of his team's performance and acknowledged that the season had taken its toll.
"We're physically exhausted, mentally drained, feeling dead because we believe it's an unjust defeat with numerous debatable incidents," the former Chelsea and Manchester United manager said. "We are dead tired, but proud. I always say you can lose a football match, but never your dignity or professionalism...
"I lost this one, but I return home prouder than ever this time. The lads gave absolutely everything this season."
Mourinho also criticised referee Anthony Taylor, adding that the Englishman showed too many yellow cards.
"It was an intense, masculine, vibrant game with a referee who seemed Spanish. It was yellow, yellow, yellow all the time," he said. "We are accustomed to the influence of referees in our games, it's nothing new, but I didn't expect it in a European final."