The Spanish side were defeated 3-2 on aggregate by the Premier League champions, losing 2-0 at the King Power Stadium in the second leg to exit the competition.
Steven N'Zonzi missed a late penalty for Sevilla to help them level the tie, while Samir Nasri was sent off for the visitors. Goals from Wes Morgan and Marc Albrighton helped Leicester to a second leg win and sent them through to the last eight.
Despite the disappointment of being knocked out, Sevilla took to Twitter to send their good wishes to Leicester for the rest of the competition writing "We wish LCFC the best of luck in the Champions League."
Leicester now await the draw for the quarter-final of the Champions League, while Sevilla turn their attentions back to La Liga.