Pedro struck the winner for Chelsea in extra time.
“Of course, I am frustrated because it was a big game, a fantastic game for us I think against a good team," said Puel at full-time. “We played well in the first half with good tempo and intensity, but it was end-to-end and we didn't have enough control of the game.
“We conceded the first goal just before the break and it was a shame because we had played well in the first half. Perhaps we can commit a little foul at the start of the move, with a little more maturity and experience. We could have managed the goal better but we came back well in the second half with more control of the game.
“We pushed this team to concede more situations and chances than they created. We came back into the game with Jamie's (Jamie Vardy's) goal. We were unlucky with the second goal also.
“It was a big disappointment because my feeling is we played very well today, with a good level on the pitch, with quality against a good team. We deserved a different result. We lost in extra time, it is harsh for my squad because they gave their best, like the fans. We didn't have the good reward at the end."
Despite the disappointment, the Foxes performed well and once the disappointment of defeat has worn off, they will still have some positivity to take going into the international break.
Puel added: “I am proud of my players because they played very well with consistency and fantastic attitude. It is good because it shows the progress of the squad and the players. They played very well in every position and they showed a good attitude. It is interesting if we can keep this positive attitude and quality on the pitch and finish the season strongly."