Goals from David Nugent and Chris Wood ended Burnley's 17-game unbeaten run, as well as an unbeaten league record at home that stretched over a year.
Leicester now lead the Clarets by six points in the race for promotion to the Premier League, but remain favourites to secure the second spot, holding a 10-point gap over QPR having played a game more.
Dyche's charges, already without injured top goalscorer Danny Ings, lost second top scorer Vokes to injury just a few minutes into the first half, leaving Burnley without the necessary firepower up front.
Speaking to Sky Sports 1, Dyche lamented the injuries to his side, saying: "Obviously we've had some challenges to our group in the build-up to the game, then we get another in the first few minutes of the game which is disappointing.
"We're missing some big players, so, all things being considered, there's a reality to it, but we'll be ready to go again next week, make no mistake.
"It's another part of the challenge of doing what you do over a season, but we've been good value so far."
On Vokes' injury, which came from an innocuous challenge as the striker appeared to tweak his knee, Dyche said: "We'll wait and see. We need to take 24 hours for it to settle down."
While Dyche was quick to hand Nigel Pearson's side their dues, he did feel that some of the decisions that referee Chris Foy made favoured the visitors over the course of the game.
"To be fair, they're a very good side, Leicester, and they're top of the league for a reason.
"They did enough to win overall.
"I thought some big decisions went their way today, and they've scored two soft goals from our point of view.
"I just thought that the second goal there was a nudge on the back, which is sometimes given in the box. It's outside the box, so why's it not a foul?"
Despite the injuries to his top two goalscorers and amidst claims that his side will struggle to get the necessary goals, Dyche appeared in typically bullish mood.
"Everyone's questioned that recently, but we've had 2-0, 3-0, and we've been putting the goals in. We don't over think these things.
"I don't think it's about spirit, it's about the quality we have in the squad. They're giving everything they can and will continue to do that."