The Foxes won the second leg 2-0 at the King Power Stadium, securing a 3-2 aggregate success.
Sevilla midfielder Samir Nasri and Sampaoli himself were both red carded in the second half, as the Leicester held firm following goals from Wes Morgan and Marc Albrighton.
Leicester goalkeeper Kasper Schmeichel saved a penalty from Steven N’Zonzi after also keeping out a Joaquin Correa spot kick in the first leg.
Sampoali told a post-match news conference, “The setback of the first goal caused the team to get cold feet.
“Their goalkeeper was very important in both matches, saving two penalties. Beyond the pain, the players have to stick with their work.
“With 10 men, we still forced Leicester back to their goal, we were all over them in the second half and created dangerous situations, but it was difficult because they were playing at home.
“I think this result is undeserved. These types of games are resolved by important details and ours were worse.”
Nasri, was sent off after clashing heads with Jamie Vardy.
Both players were booked for the confrontation, but it was Nasri’s second yellow of the game.
He added, “Nasri? He contributed a lot when he was on the pitch.
“I don’t know about his red card, I was very far away from it and I couldn’t see him, but I hope he stays because he brings us a lot going forward.
“My dismissal? I don’t know why it happened. I think the fourth official got it wrong because all I did was complain about a bad goal we conceded.
“I see myself going to bed in pain tonight, thinking that a dream has gone.”