The visitors gave a good account of themselves but were unable to break the hosts' stubborn defence, eventually leaving White Hart Lane empty-handed.
Puel told BBC Sport: "It was strange. In the first half without pressure we took two goals and it is difficult to accept this.
"In the second half we came back with good attitude and scored quick. At 2-1 there was a possibility to come back. In the end a draw would have been normal. It is disappointment. It was difficult for us but also for Tottenham."
Up next for 10th-placed Southampton is a south coast derby against Bournemouth after the international break.