Llorente struck two minutes from full-time to earn Athletic a 3-1 victory over Sporting Lisbon in last night's [Thursday] semi-final second leg at San Mames and seal a 4-3 aggregate victory for the Basque side.
An emotional Llorente broke down in tears at the final whistle as his side booked a final showdown with Primera Division rivals Atletico Madrid in Bucharest next month - Athletic's second European final after finishing runners-up in the 1977 UEFA Cup.
He said: "The truth is that what happened in San Mames is incredible.
"It's the first time that I've cried while playing a football match."
The Spanish World Cup winner added in AS: "Without doubt, it's the most important goal that I've scored in my entire career. It's got us into a final and with that we've also gone down in history.
"But now we have an opportunity to win the tournament and hopefully we can continue contributing to making this history even greater."