Jamie Vardy converted a late penalty to cancel out Bernardo Silva's 26th minute opener but the Foxes were stung again - this time 4-3 in a shootout - denying them qualification to the last four.
With seven changes, Puel's starting XI included several unusual faces, including Ghana defender Daniel Amartey, who made just his fifth appearance in all competitions this season.
“For me, it was a fantastic game,” Puel said, as reported by his club's official website.
“It was a fantastic scenario, all the game, until the end. Penalties are penalties. It was not for us.
“It’s a disappointment. But I have no regrets about our players, our game. All the players gave their best. It was competitive game between two good teams.
"It was encouraging for the future. We have to keep this high level of performance. It was a good response after our last game on Saturday."
Vardy, briefly, looked like emerging Leicester's hero of the night following his stoppage time equalizer, but the England striker was unlucky with his kick in the shootout, as was Riyad Mahrez.
“I know about my players and the quality they can make on the pitch and we deserved another goal to win," Puel added.
"We had more chances than the opponent to win the game.
“I want to speak about our game because it was a fantastic game and there was good quality and we deserved a different result at the end.
"It’s a disappointment for the whole squad. We tried to win this game, with good quality, and a positive outlook. This is a good feeling for the future.”
Leicester will hope to bounce back when they host another Manchester side - this time United - in the Premier League on Saturday.