Coventry went down by two goals to nil after a disappointing display at the Walkers Stadium.
Steve Howard netted early in the tie, while substitute Barry Hayles made it 2-0 late on as a new-look Leicester side dominated against a below par Sky Blues.
The home side started brightly and City had two lucky escapes in the opening five minutes as Leicester's new Hungarian midfielder Zsolt Lacko - one of five new arrivals at the Walkers Stadium to be named in the starting line-up - wasted two superb chances to give his team the lead.
Firstly he headed wide from eight yards out with no City defender to be seen, before he blazed a 15-yard shot well over the bar.
But it only took until the eleventh minute before Leicester took the lead, January signing Steve Howard slotting his shot through Dimi Konstantopoulos' legs after he was played through by the impressive Laczko to give the Foxes a deserved one-goal advantage.
The Sky Blues could and should have been level in the 15th minute when Leon Best nicked in to win a throughball ahead of Foxes new keeper Alnwick but when the ball fell to Dele Adebola his shot hit the foot of the post and went wide.
But on the whole the Sky Blues were just not at the races in a first half predominantly dominated by Ian Holloway's charges. At times City were simply unable to get the ball for any amount of time and could have been further behind had their opponent's other Hungarian import Gabor Bori not shot over the crossbar with 35 on the clock.
Towards the end of a poor opening period for City, Iain Dowie was forced into a change as Chris Birchall - making his first City start of the season - hobbled off to be replaced by Robbie Simpson.
The Sky Blues were guilty of giving the ball away with alarming regularity during the first 45 minutes and the opening exchanges of the second half indicated that nothing had changed.
But when Mifsud got a rare opportunity to utilise his explosive pace down the right flank, he won a free-kick and Simpson should have done better with a free header from Kev Thornton's delivery - his effort going harmlessly wide.
City were looking more useful as an attacking outfit but Konstantopoulos had to get down smartly to a Matt Oakley volley in the 64th minute, tipping the former Derby midfielder's shot around the post as it bounced awkwardly in front of him. The Greek keeper than produced another good save from Iain Hume to keep the Sky Blues in it.
With just under 20 minutes remaining Kevin Kyle replaced Best up front although it was the Foxes who were continuing to do the majority of the pressing, threatening to double their lead and kill the tie off. Liam Davis came on for Thornton in what was Iain Dowie's final switch - the livewire midfielder having had a quiet afternoon.
Ian Holloway made his first switch of the game with ten minutes left on the clock, bringing on another of his new signings, striker Barry Hayles.
And it was veteran striker who made it 2-0 to Leicester in the 85th minute, taking advantage of a defensive error by Ben Turner and slotting the ball past Konstantopoulos and into the back of the net, despite Turner's best efforts to track back and clear off the line.
Leicester: Alnwick; Stearman; Kisnorbo; McAuley; Mattock; Bori; Oakley; Clemence; Laczko (Hayles 81); Hume (Wesolowski 90); Howard. Subs (not used): Fryatt; N'Gotty; Chambers.
Goals: Howard (11), Hayles (85)
Booked: Kisnorbo (54)
Coventry: Konstantopoulos; Osbourne; Ward; Turner; Borrowdale; Mifsud; Thornton (Davis 78); Hughes M; Birchall (Simpson 38); Adebola; Best (Kyle 71). Subs (not used): Page; Hildreth.
Goals: None
Booked: None
Referee: Mr M Atkinson
Attendance: 23,905
