Valentine Eysseric and Renato Civelli scored the goals that saw Les Aiglons close the gap on third-placed Marseille to just one point.
The French tactician said that his team should have put the game beyond doubt before Civelli scored with six minutes remaining.
He also believes that the red card shown to Reims full-back Aissa Mandi helped his team to score the killer goal.
"I would have liked more serenity," Puel told reporters. "[Reims] tightened defensively after the break. We lacked fluidity in the second half.
"The red card helped us regain control of the game and score the second goal. Congratulations to the players as the game was far from clear."
Nice make the trip to play Saint-Etienne next Saturday.