With the Foxes trailing 1-0 – despite creating the better chances – Vardy came off the bench to step up from 12 yards with his first touch, after Jan Vertonghen fouled James Maddison.
But Hugo Lloris saved from the striker and Leicester subsequently slumped to a fourth defeat in five league games.
That moment proved a turning point in the encounter, as moments later Christian Eriksen doubled Spurs’ advantage.
Speaking after the game, Puel said: “Normally it’s Jamie to take the penalty. I gave him the opportunity to shoot this penalty. I said to him he can take it.
“But it’s not just the penalty, it’s all the game. We had all the opportunities to lead this game or to get back into the game.
“We had a lot of chances.”
Puel’s decision to leave Vardy on the substitutes’ bench and start winger Demarai Gray up front has drawn plenty of criticism – while the relationship between the pair is also in question.
And although Vardy did net to make it 2-1, the Frenchman defended his use of the 32-year-old.
“I was happy with the performance of Demarai Gray. I also liked to see the other option of Jamie too.
“Today we needed to have another option, not just Jamie.”