Toiling domestically and beaten 2-1 in the first leg of the last 16 tie, Leicester roared back to win 2-0 in Tuesday's return leg, sending them into Friday's last-eight draw.
Shakespeare was promoted following Claudio Ranieri's dismissal, feels the feat stands "right up there" with last season's fairytale Premier League title win and said there could be more miracles still to come.
"We know there's going to be some terrific teams, as in the previous round," said Shakespeare, who was taking charge of only his fourth game as a manager.
"We have to be delighted with the performance in knocking Seville out, because their record in Europe is there for everyone to see.
"But we're in there on merit, make no mistake about that. We might just be the surprise team. "But we know the quality of teams in there is getting down to the real serious business now."
Barcelona, Real Madrid, Bayern Munich and Juventus are among the teams who have already reached the quarter-finals, but Shakespeare said he had no preference regarding Leicester's next opponents.
Asked if there was a team he was hoping to come up against, he smiled and replied simply: "No." Ranieri had been sitting in the away dug-out for Leicester's defeat in the first leg three weeks ago, only to be dismissed by the club's Thai owners upon his return to England.
The away goal scored by Jamie Vardy at the Ramon Sanchez Pizjuan sowed the seeds of Leicester's second-leg revival and Shakespeare acknowledged Ranieri's role.
"Claudio will always be fondly remembered by everyone at this football club for what he achieved and helped us achieve," Shakespeare told reporters in the King Power Stadium press room.
"The performance in the first leg, when Claudio was in charge, gave us the springboard for the result tonight."
The King Power rocking in a way that recalled the giddy final weeks of last season, captain Wes Morgan levelled the tie on aggregate by kneeing Riyad Mahrez's 27th-minute free-kick past Sergio Rico.
It put Leicester in front on away goals and they took the lead outright through Marc Albrighton in the 54th minute, moments after Sergio Escudero had left the home side's crossbar quivering.
Sevilla lost Samir Nasri to a second red card for aiming a headbutt at Vardy before Leicester goalkeeper Kasper Schmeichel took centre-stage.
The Denmark international conceded a penalty for catching Vitolo with an attempted block, but with Steven N'Zonzi poised to send the tie to extra time, Schmeichel plunged to his left to save.
Sevilla coach Jorge Sampaoli, who was sent to the stands at the death, said he did not know why Italian referee Daniele Orsato had opted to dismiss either Nasri or himself.
Sevilla had also squandered a penalty in the first leg, Schmeichel thwarting Joaquin Correa, and Sampaoli concurred when it was suggested his side had a "psychological problem" with spot-kicks.
Sevilla have seen their La Liga title hopes fade after successive 1-1 draws against Alaves and Leganes and Sampaoli said fatigue may have been a factor in their Champions League exit.
"It's hard to compete on two fronts in the league and the Champions League. That creates a certain amount of stress," said the Argentine.
"But even so, we still managed to dominate this game in terms of possession, as we did in the first leg. "Games can turn on little things. Escudero went close and they went and scored the second goal, which was decisive."
Sevilla had hoped to kick on in the Champions League after three successive Europa League triumphs, but Sampaoli said it was inaccurate to talk about failure.
"The fault lies at the feet of the manager. I pick the side," he said. "But I'm really proud of the effort my boys put in tonight."