Leicester remain in 10th position in the Premier League standings, while Burnley are 15th but just a point above the relegation zone.
Tributes to Srivaddhanaprabha and the four other people who lost their lives in the helicopter crash on October 27 dominated the build-up to kickoff, but Leicester were able to start brightly with Wilfred Ndidi seeing a long-range strike tipped wide by Joe Hart.
The home side went close again on the quarter-of-an-hour mark through Jamie Vardy, who saw a shot cleared off the line by Matthew Lowton after Burnley had failed to deal with a cross from the right flank.
Leicester remained in the ascendancy, however, and the East Midlands outfit again went close midway through the first half when Rachid Ghezzal powered a header against the crossbar after being found by Marc Albrighton.
Demarai Gray was the next Leicester player to make an impact in the final third, but Hart came out well to make a timely block from the winger after he had been teed up by Vardy.
Burnley grew more into the game as the opening 45 minutes drew to a close and Johann Berg Gudmundsson tested Schmeichel with a 30-yard free kick, but Dyche would have been relieved to get his team back in the changing rooms without going behind.
The Clarets went onto the front foot after the restart but it was Leicester who created the first opportunity of the second period, with Albrighton seeing a deflected shot from 14 yards blocked by Hart.
Jonny Evans saw a header kept out by Hart at the back post, while Wood should have opened the scoring for Burnley at the other end only to slice a volley over the bar from 12 yards out.
Substitute Shinji Okazaki almost won it for Leicester in added-on time, but after the Japanese had headed marginally wide of the post referee Mike Dean called time on the game as Burnley became the first team to stop Leicester from scoring in a Premier League fixture this season.
LEICESTER CITY (4-2-3-1): Schmeichel; Pereira, Morgan, Evans (Soyuncu 90'), Chilwell; Ndidi, Mendy; Gray (Okazaki 84'), Ghezzal, Albrighton (Iheanacho 60'); Vardy
BURNLEY (4-4-2): Hart; Lowton, Long, Mee, Taylor; Lennon, Cork, Defour (Hendrick 55'), Gudmundsson (Brady 65'); Vokes (Barnes 73'), Wood