Antonio Conte has warned his stars to cut out their mental instability if they want to reach the top four.
The Tottenham boss watched his men twice throw away the lead before they were beaten by Che Adams' late winner to cap an outstanding Southampton display.
Conte said afterwards: “We have to improve. If we want to grow and be competitive, the first thing you have to improve is stability.
“Not up and down, up and down. We have to improve. Also, in a team it is important to have players with experience to manage the situation during the game.”
Spurs led after 18 minutes through Jan Bednarek’s own goal before the Saints hit back through Armando Broja, who netted his eighth of the season in the 23rd minute.
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But Son Heung-min put the home side back in front with 20 minutes left - only for James Ward-Prowse to set up two late goals for Elyanoussi and Adams with two fabulous crosses.
Tottenham remain seventh, four points off the top four, while Southampton climb to 10th.
Southampton boss Ralph Hasenhuttl, celebrating his 500th game as a manager, said: “I will never forget this. It is good to leave with a positive result here. Our last two games were against Man City and Tottenham and now we will play against Manchester United on Saturday.
"I would have been happy with a point because of the chances we created. We believed in us and the mentality and character of the team is outrageous, it is fantastic to watch, they are fighting for everything. We played fantastic football and played 23 passes before the second goal. Fantastic.
"You can play the ball round the box but the decisive ball is the last one into the box. Che Adams made a super header, super beautiful goals. The whole performance was by far the best since I was here.”
