Spurs themselves were awarded a spot kick when Steven Davis brought down Dele Alli inside the area shortly after the half-hour mark, but referee Andre Marriner was unmoved when Dusan Tadic was caught by Ben Davies on the stroke of half time.
Replays suggested that Southampton had a case, and Puel believes that his side deserved more than the 2-1 defeat that was inflicted upon them.
"If the referee gives a penalty for their second goal then he needed to give a penalty for us," he told reporters.
"I cannot see the difference. Two teams were at the same level. It was difficult for the two teams to find opportunities. Each team tried to play good football, without a lot of opportunities, but I think we stayed with a good spirit. A draw seems normal for me."
The defeat leaves Southampton still 10th in the Premier League table.