The Seagulls striker was the hero at the weekend as they beat Arsenal 2-1 at home but squandered a golden opportunity to give his side another three points.
Aaron Connolly won the spot kick when he was clumsily brought down by James Justin in the 14th minute.
Schmeichel easily saved down to his right with Maupay's shot not finding the bottom corner.
Brighton enjoyed the better of the chances in the first half with Aaron Mooy and Lewis Dunk both having efforts blocked while they did lose Adam Webster who had to come off due to an injury.
The second half saw few opportunities for either team as Leicester dictated possession but were wasteful with their efforts on goal.
There was an appeal for handball deep into stoppage-time as Jamie Vardy's header hit Brighton captain Lewis Dunk, but to no avail.
The points were shared at the King Power Stadium with Brighton putting more daylight between themselves and the relegation zone while Leicester now have a four point cushion over fourth placed Chelsea.
Leicester and Brighton played out a 0-0 draw at the King Power Stadium on Tuesday night with Neal Maupay missing from the penalty spot early on.