The Danish keeper dived to his left to push away a Glenn Murray spot-kick, which had been awarded after Wilfred Ndidi fouled Jose Izquierdo. Buoyed by the save, the Foxes went on to win thanks to goals from Vicente Iborra and Jamie Vardy.
“It was a good score for us to be 0-0 at half time," Puel told LCFC TV. "It was important to come back with ambition after half time and it was better with good balance.
"I think the save from Kasper Schmeichel was the turning point of the game because it gave us a good boost, but it was the opposite for the opponent. It was a difficult situation for them to accept and then we scored a fantastic goal."
Ndidi was shown a second yellow card for a foul on Shane Duffy with the score at 1-0, a decision the Nigerian evidently disagreed with.
"With the sending off, we had to resist," said Puel. "I wasn’t happy with the first half but I was happy with the direction we went in the second half, and also the three points.
"These three points are crucial going into the next games.”
Leicester are challenging Burnley for seventh spot, which could be enough for a Europa League place depending on who wins the FA Cup. The Clarets are currently three points clear of Puel's team.
The Foxes host Newcastle next weekend before the crunch match against Burnley the week after.