Vardy has withdrawn himself from the selection frame due to the unlikely prospect of dislodging Harry Kane as Gareth Southgate's preferred centre-forward and a desire to spend more time with his family.
The 31-year-old believes the time is right for younger players to be given an extended opportunity, although he could still add to his 26 caps in the event of an injury crisis.
Leicester are poised to benefit from the lighter demands on their key striker, but Puel remains uncertain about his player's decision.
"We discussed it about two or three weeks ago," the Foxes boss told reporters after beating Fleetwood Town in the Carabao Cup second round.
"He took his decision and we have to respect it.
"I'm just a little sad about his decision because for fans of the national team it was a fantastic feeling to see him playing.
"But we have to respect his decision and now he dedicates his time to his club and will continue to give his best and hopefully win a trophy."
Vardy admitted it was difficult to walk away from his country but felt it was the right time to do so.
Talking to The Guardian, he said: "To be honest with you, this has been on my mind for a while.
“I’m not getting any younger and you can see, to be fair to the gaffer [Gareth Southgate], he wants to make it more youthful, which obviously had its benefits during the World Cup – we got to the semi-finals and finished fourth, which is equal to the furthest we have ever been on foreign soil.
“So I just said to Gareth that I think it’s probably best from now on, especially with the way he wants to go, to bring youngsters in who he thinks have got the ability and start nurturing them into international football.”
Vardy will sit out the Premier League clash with Liverpool on Saturday as he serves the final match of a three-game suspension.