The England international was given his marching orders 20 minutes into the second half for a lunge on Matt Doherty, who left the field injured.
Puel has questioned whether a red card should have been shown by referee Mike Dean, but is hopeful that others will now step up with Vardy banned for Leicester's next three matches.
"I think it perhaps was a little tough, because it was not his intention to make a foul," he told BBC Sport. "He touched the ball. After that, he was perhaps too enthusiastic on his move, on his tackle. It's a pity.
"I want to support him. He likes playing all the time, 90 minutes if he can, and we need now to find a solution to replace him and it will be a good opportunity for some other player to show their quality."
Vardy will miss games against Southampton and Liverpool in the Premier League, as well as the EFL Cup second-round tie against Fleetwood Town.