The 21-year-old came off the bench against Switzerland on Tuesday as England won 1-0. The match was played at Chilwell's home stadium for Leicester, the King Power.
Puel was delighted with the youngster's selection, but warned that he would have to be consistent to continue to play internationally.
"It will be the choice for Gareth," Puel said. "But of course it is a fantastic feeling for him because it is an acknowledgement for him to carry on his hard work and to keep a good consistency.
"It is also a good feeling for all the club. It is a good reward for the player, the trainers and manager who have worked with him. I am also happy for Demarai."
Demarai Gray was an unused substitute, and he along with Chilwell and Harry Maguire made up the three Leicester players in the England squad.
"The internationals have come back with a smile. They were happy to come back as a team," Puel continued.
"We had 13 international players away and I am happy because they came back with a good mentality. Now of course it will be important for them to have a good focus and desire for their club."