The visitors had led through Riyad Mahrez's header midway through the first half at Vicarage Road, but were pegged back on the stroke of half-time by a tap-in from Molla Wague, who spent the second half of last season on loan with the Foxes.
With 25 minutes remaining, Abdoulaye Doucoure stretched to keep Tom Cleverley's free-kick in play and sent the ball across goal, where Schmeichel fumbled it over the line as the Hornets claimed a first Premier League win in seven.
"All the team are responsible for the free-kick," said Puel, in quotes reported by BBC Sport.
"We didn't concede a lot of chances. It was difficult to defend against this team with long balls and second balls. They're a physical team.
"It's a shame. It was an interesting game. It's a story about free-kicks. Our first half was not bad with some quality and chances. We conceded the goal from the free-kick [corner] just before half-time.
"In the second half it was more difficult. This result is a little harsh. It was not a bad game for us.
"Unfortunately we cannot come back into the game with two or three chances at the end. It's a story about free-kicks and we need to correct this."
Puel's opposite number Marco Silva remained level-headed in victory as Watford brought an end to a run of just one point from the past six matches.
"We didn't lose our focus when we weren't winning, and now that we have won, I'm not the happiest man in the world," he said.
"I know clear what is our reality as a club. You can have some fantastic results in a row but a season is too long.
"I know what can happen if you have lots of players banned or injured. I know that — our players know. It’s impossible to win all our matches."