Roma lost in a penalty shootout on Wednesday night after scores were locked at 1-1 at the end of extra-time.
Llorente said, "Mourinho told us that we have to be proud of what we did, that we left everything on the pitch. There is pride; penalties are a lottery and it didn't go well for us. It's a very sad day for all Roma fans, very sad. But we gave everything."
Meanwhile, teammate Bryan Cristante also stated: "There is a lot of disappointment and it will be like that for a few days. But then we have to start again. This remains a great group and we have done something great by making two finals in a row.
"You don't get to a Europa League final by chance. The pride remains for this great team that has shown it is strong and up to it."