Spurs let a 3-1 lead slip against struggling Saints, and as a result missed the chance to go third in the Premier League table.
Goals from Pedro Porro, Harry Kane and Ivan Perisic made it look like Spurs were set to move into the Champions League spots, but bottom-of-the table Southampton fought back with a Theo Walcott goal and James Ward-Prowse's stoppage-time penalty sealing a point.
Conte conducted a furious post-match interview, saying: "If we are going to discuss the penalty, it means we don't want to see the other situations. I think it's much better to go into the problem because the problem is that, for another time we showed that we are not a team.
"We are 11 players that go into the pitch. I see selfish players, I see players that don't want to help each other and don't put their heart (in).
"Why? Because they are used to it here, they are used to it. They don't play for something important yeah. They don't want to play under pressure, they don't want to play under stress.
"It is easy in this way. Tottenham's story is this. Twenty years there is the owner and they never won something but why? The fault is only for the club, or for every manager that stays here. I have seen the managers that Tottenham had on the bench."
As a result, Conte has been hacked down to odds-on 1/5 with several bookies to be next manager to get sacked, when he was as high as 6/1 to get the boot just two weeks ago, and 3/1 before the weekend began.
West Ham boss David Moyes is second favourite at 13/2, and might enjoy not having the spotlight on him until the Irons' next crucial clash against Southampton on Sunday, April 2.
Brendan Rodgers has been pushed out to 10/1 after Leicester drew 1-1 at Brentford while Chelsea boss Graham Potter (14/1) is next in the betting ahead of Forest boss Steve Cooper at 16/1.
Former Spurs boss Mauricio Pochettino has been installed 6/4 favourite to be the next permanent Tottenham manager, with Luis Enrique (6/1) and Marco Silva (10/1) next in the market.