James Ward-Prowse gave Southampton the lead with a spectacular strike in the first half but Spurs were able to draw level when Mohammed Salisu gave away a penalty and was sent off. Harry Kane slotted the spot-kick into the net.
Despite their numerical advantage for most of the game, Spurs were unable to capitalise.
"Disappointed especially after they went down to 10 men. We've got to win the game and we couldn't do that," Eric Dier said after the game.
"They defended very well and fought for each other but that doesn't matter from our side of it. We have to be able to break them down. We weren't good enough at doing that.
"We've got to keep things in perspective. Everyone can see the progression."
Southampton took the lead after 25 minutes when Dele Alli failed to clear a corner and Ward-Prowse hit a left-footed shot into the net.
However, their lead only lasted until 41 minutes when Salisu fouled Son Heung-Min in the box. He was red carded and Kane hit the penalty with force into the goal.
Kane did find the net again early in the second half but it was not awarded as he was deemed offside.
West Ham United's 4-1 win at Watford meant that Tottenham dropped to sixth on 30 points, one point behind David Moyes' side and five behind fourth-placed Arsenal, but with two games in hand over both. Southampton are 13th with 21 points.