Steve Howard and Barry Hayles marked their home debuts with a goal apiece.
Howard took only 11 minutes to open the scoring, collecting Iain Hume's pass before shooting through the legs of Dimi Konstantopoulos at the near post.
Dele Adebola should have equalised but rolled his shot against the outside of the post with the goal at his mercy.
Substitute Hayles sealed Leicester's win when he capitalised on a defensive mistake by Ben Turner to race clear and slide the ball under Konstantopoulos.
Leicester boss Ian Holloway:
"I need to add and create competition in certain positions, and once we have that we will be rocking and rolling," Holloway said.
"A week is a long time in football and this next week is going to be a very long time for everybody.
"We've got to do a microwave pre-season with these boys, and when more arrive, they'll understand what I mean."
Coventry boss Iain Dowie:
Iain Dowie apologised to Coventry fans for his side's 'abject'performance in the 2-0 defeat to Midlands rivals Leicester at the Walkers Stadium.
"It was a very poor display," said the unhappy manager. "It was abject and a million miles below par.
"We have let a fantastic travelling support down badly.
"They came here in numbers expecting a performance against our local rivals and we had no guile and no craft and I have to say sorry for that."
Leicester: Alnwick, Stearman, McAuley, Kisnorbo, Mattock, Bori, Oakley, Clemence, Laczko (Hayles 81), Hume (Wesolowski 90), Howard.
Subs Not Used: James Chambers, N'Gotty, Fryatt.
Goals: Howard 11, Hayles 85.
Coventry: Konstantopoulos, Osbourne, Ward, Turner, Borrowdale, Birchall (Simpson 38), Michael Hughes, Thornton (Davis 78), Mifsud, Best (Kyle 71), Adebola.
Subs Not Used: Page, Hildreth.
Ref: Martin Atkinson (W Yorkshire).