Jamie Vardy scored the only goal of the match as Leicester ensured that they would be present when the draw for the final eight of the competition is made.
Puel has admitted that "it was difficult to find space" against the Championship visitors, but the Frenchman was just pleased to progress to the next round.
"Tough game against a good team. It was difficult to find space. For the first 30 minutes the tempo was too slow, but the second half was good for us," Puel told reporters.
"We had to concentrate late in the game and Kasper [Schmeichel] made a very good save. It would have been more comfortable with more than one goal, but the important thing was to win."
Chelsea joined Leicester in the quarter-finals courtesy of their 4-0 win over Hull City at Stamford Bridge.