Vardy announced that he was stepping aside from England duty on Tuesday in order to allow manager Gareth Southgate ot include younger players in his upcoming squad.
A latecomer to international football, Vardy has scored seven goals in 26 games for his country, though he could still return to the fold in the even of an injury crisis.
A desire to spend more time with his family and extend his club career also played a part in the 31-year-old's decision and Puel says that he can understand why Vardy has done what he has done.
"We discussed it about two or three weeks ago. He took his decision and we have to respect it," he said after the Carabao Cup win over Fleetwood on Tuesday night.
"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."