The Frenchman looked on course to mark his first season in English football with a surprise triumph after Italian Manolo Gabbiadini's double saw Saints roar back from 2-0 down, only to suffer heartbreak when Zlatan Ibrahimovic headed a late winner.
It was rough on Southampton who had another goal for Gabbiadini ruled out for offside when it was 0-0 although TV replays suggested it should have stood. Minutes later, Ibrahimovic scored the opener with a sublime free kick.
"The scenario was cruel in the end. We started the game very well and we scored, but the decision of the referee was very hard to accept," former Monaco and Lyon coach Puel said.
"Manolo Gabbiadini scored three good goals. There's a lot of disappointment, of course. We had a fantastic game without the reward. I hope we can continue on this level.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"We played a fantastic game and before their third goal we had lots of chances and situations to win the game. We came back with quality. Perhaps we deserve better."
United manager Jose Mourinho echoed Puel's opinion, saying it had been a "tricky" final and that Southampton deserved at least to take the match into extra time.
"I was more afraid of this final than the other ones because in the others another giant is on the other side," he told reporters. "Southampton are not Manchester United but they have good players and a good manager.
"They did fantastic work. They deserved to have extra time. To lose in the 87th minute with no time to come back was a bit unfair for them. They gave us a beautiful final."
Mourinho said Southampton's extra freshness, courtesy of a two-week window without a game leading up to the final, nearly proved decisive.
Since Southampton's last game, United have been involved in the FA Cup and a two-legged Europa League tie.
"I think they were in Spain, they were quiet, working and preparing," Mourinho said. "We were playing and travelling. The moment the game was broken at 2-2 they had an advantage.
"I think we were lucky to be 2-0 up.
"Gabbiadini's execution for the second goal was phenomenal. But in the end we coped because we are humble and stuck together. We had a bit of luck."
(Reporting by Martyn Herman, editing by Neil Robinson)
