Spurs were denied by the video review system as they chased the three points at St Mary’s after Harry Kane’s penalty had earlier cancelled out James Ward-Prowse’s stunning opener for Saints.
Ward-Prowse found the far corner with a first-time effort in the 25th minute but Kane rifled in from the spot after Son Heung-min was chopped down five minutes before the break by Mohammed Salisu, who was shown a red card.
It was all Spurs in the second half and Kane saw a goal cancelled out for offside, which did not look obvious on VAR, and then referee Anthony Taylor adjudged Fraser Forster to have been fouled when he dropped the ball under an innocuous challenge from Matt Doherty.
“Yeah, I think Harry scored twice, one a penalty and then the second goal. I think that I don’t want to comment on the referee decision or the VAR decision,” Conte said.
“They are there to try to do their best. We hope every time that they make the best decision.”
On his side’s inability to get past 10 men in the second half, the Italian added: “My demands are very high because I am used to being competitive and to win, and for sure for me there is a big disappointment when we don’t win.
“I understand also the situation. Now for sure we have to work a lot and it won’t be easy to fight for something this season.
“We need to improve a lot. For sure it was an opportunity that we missed. When you have this type of situation you have to try to exploit, to try to get three points.
“We knew very well that to play against Southampton in this stadium is not easy. The situation at one point of the game was positive for us.
“We didn’t find the solutions to score. We scored, but they decided to disallow the goal.”
Ralph Hasenhuttl was full of pride for his side’s rear-guard display with 10 men, having been the better side when the numbers were equal.
“I am super happy about what I have seen, the atmosphere we had today was one of the best since I have been here, (the fans) pushed us, they were fighting with us,” the Austrian said.
“I said we have been so good first half and when you are fighting and working hard, been against all the issues we have with Covid cases, with 48 hours between games and when you are with 10 men for 60 minutes, I cannot be more proud of them, two days after such a game against West Ham.
“The brave guys get rewards and we got the point today.
“Everything was working today, the lads were convinced and everyone from the first moment was putting everything on the pitch. It is hard to prepare for games because we never know what will come up.
“We have a team you can really identify with, young lads, getting better. This is so enjoyable to work with them every day, young and with potential.”