After a goalless draw in the first leg, manager Brendan Rodgers made four changes to the side that beat Aston Villa on Sunday, with Daniel Amartey, Hamza Choudhury, Cengiz Ünder and Marc Albrighton returning to the XI, while midfielder Wilfred Ndidi made his 150th start for the Football Club in all competitions.
Just over 90 seconds into the second leg, Çağlar Söyüncü drove from centre-back and through midfield before slicing fellow Turkey international Ünder's deflected effort wide, while Ünder fired off target shortly after following two early opportunities in Leicester.
Slavia stopper Ondřej Kolář was called into action with 10 minutes on the clock, this time denying the lively Ünder's low drive as City maintained their momentum in the opening stages, while Söyüncü stood in the way of Nicolae Stanciu's long-ranger and Albrighton curled over in the minutes that followed.
On 19 minutes, Peter Olayinka nearly turned the ball into his own net after Jonny Evans returned Albrighton's corner back across the face of goal, but Kolář was on hand to spare the Slavia striker and held on his line.
The Northern Ireland defender turned provider eight minutes later, feeding Albrighton in the right channel, only for the winger's strike to be comfortably collected by Kolář, who was untroubled by the attempt.
The Czech side, who sit top of their division, responded and when Senegalese striker Abdallah Sima latched onto a long ball, he drilled a first-time effort narrowly wide of Kasper Schmeichel's right-hand post.
Kolář gathered a half-volley from Ndidi with 12 minutes of the first half to play, as the visiting side continued to limit City to half chances before the interval, while a brilliant recovery run and interception from Ünder at the other end halted a Slavia attack before it could come to fruition.
Červenobílí’s next attack, on 39 minutes, saw Jan Kuchta nod wide at the near post before Kolář swallowed up a Jamie Vardy cross from the left and Choudhury had a penalty appeal turned down as a largely uneventful opening 45 minutes reached a climax.
Jakub Hromada miscued from close range just after the match resumed, but Slavia's pressure at the start of the second half paid off when Lukáš Provod side-footed home at the far post from a deep delivery to net an away goal for his outfit.
That meant the tie would be settled in the regulation 90 minutes at Leicester City Stadium, and with 51 minutes on the clock, Vardy slipped in Ünder, but he could only fire the wrong side of the post from a tight angle while under pressure from two Slavia defenders.
Just after the hour-mark, Rodgers made a triple substitution as Timothy Castagne, Ricardo Pereira and Harvey Barnes were all introduced in a bid to turn the tie on its head. Albrighton, Amartey and Choudhury all made way.
Leicester began to occupy the Slavia half after the switch in personnel, and it nearly immediately paid dividends when substitute Ricardo had the ball in the net, only for Vardy to be penalised for handball in the build-up.
But for all of City's positive play, Sima drilled in from distance to double Slavia's advantage, ultimately leaving the hosts needing to score three goals to progress to the Round of 16 stage.
The Foxes' fourth change followed with 10 minutes remaining, as 19-year-old midfielder Sidnei Tavares came on for his first team debut for the Football Club, replacing Ünder.
City were unable to conjure up any significant goalscoring opportunities in the closing stages, though, and Slavia Prague ran out 2-0 winners on Filbert Way.
Major moment
After nearly 140 minutes of goalless football, Slavia Prague were the first to strike in the second leg on Filbert Way, meaning City needed to score twice to avoid being knocked out at the Round of 32 stage.
However Abdullah Sima added to Lukáš Provod's 49th-minute strike and it was Slavia who booked their spot in the Round of 16 with a 2-0 triumph.
Who impressed?
Speaking on LCFC Radio’s Matchday Live, Matt Elliott said: “I’m going to give it to Jonny Evans because he didn’t do too much wrong. I don’t think anyone played at the top of their game, but fair play to Slavia Prague. They deserve this moment."
Coming up…
Leicester City contest a second home fixture in the space of four days when they welcome Arsenal to King Power Stadium in the Premier League (12pm GMT kick-off), before back-to-back away trips to Burnley and Brighton & Hove Albion follow next week.