Sevilla held a 2-1 advantage going into the second leg against the 'Lions' at San Mames on Wednesday, but were swept aside 3-0 on the night to miss out on the final.
Del Nido, whose pre-match remark that "we are going to eat the lion from its mane to its tail" was given widespread media coverage, had to endure a torrid time from Bilbao fans as they taunted him towards the end of the game.
"I'm quite capable of handling the pressure," del Nido told the Sevilla website. "I wish all the pressure was on me.
"I tried to achieve two things with my words. One was to convince my players that we could handle the hostile atmosphere, and the other was to focus the fans' attention on the game, and I achieved that.
"I don't regret it. All I regret is that we didn't beat Athletic."
Athletic set up a final meeting with Primera Liga leaders Barcelona, who eliminated Real Mallorca, sparking wild celebrations on the pitch at San Mames and later in the streets of Bilbao.
"It's incredible. I'm never going to be able to forget what I have just experienced on the pitch," Javi Martinez, scorer of Bilbao's first goal, was quoted as saying in sports daily AS.
"The fans were right behind us all day and we knew we had to do everything we could to get to the final, and now we have done it."
The Basque club's love affair with the tournament has seen them win the cup 23 times, one less than record-holders Barca.
They last lifted the trophy in 1984 when they beat Barca 1-0 at the Bernabeu.
