The Saints found themselves 2-0 down at half-time at White Hart Lane after goals from Christian Eriksen and Dele Alli, the latter coming from the penalty spot.
Puel had no qualms with referee Andre Marriner's decision to award Tottenham a penalty but could not understand why the official did not hand his side a spot-kick when Ben Davies brought down Dusan Tadic just before the break.
"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."
Southampton did manage to pull a goal back after the interval through James Ward-Prowse and had Spurs on the back foot at times, prompting Puel to suggest they should have at least claimed a share of the spoils.
"Two teams were at the same level," added the Frenchman. "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."