Schmeichel came charging off his line on the stroke of half-time in extra-time, making it a more straightforward task for Pedro to nod in N'Golo Kante's speculative cross and give Chelsea a place in the FA Cup semi-finals.
The Denmark international was earlier beaten by Alvaro Morata's first goal since Boxing Day before Jamie Vardy's second-half leveller sent the last-eight tie beyond the 90 minutes.
Puel told BBC Sport: "I think since the beginning Kasper has been a fantastic goalkeeper. In goal there is always a mistake, but he has been fantastic.
"I can't say anything wrong about him — he's a fantastic keeper. We are unlucky today."
Puel felt his side deserved more from an entertaining encounter, adding: "I'm a bit upset at the moment because I think we deserved another result.
"They found a good clinical edge. Morata's goal was the only chance of the first half, it was harsh to concede just before half-time. But we came back with more calm and more quality.
"I'm proud of my players because it was a game with a high level against a good team. We improved and we deserve another result."