Jermain Defoe put Sunderland ahead with six minutes to play, but Virgil Van Dijk's injury-time strike secured Saints a 1-1 draw, denying the visitors a seventh league win of the season.
Sunderland now sit just a point above the drop zone with nine games to play, with beleaguered manager Allardyce admitting the Black Cats shot themselves in the foot at St Mary's.
"We're scoring goals but our problem is clean sheets, and it's a massive problem for us," said Allardyce.
"We've got to keep them sooner or later.
"It was going to be my first 1-0 win that I was going to celebrate with my family on Mothers' Day tomorrow, and it would have been unbelievable.
"But now I'm going to be crying into my wine, I'll tell you that now.
"I'm not going to be very happy and sadly I hope I don't take it out on my grandkids, but I'll try not to.
"A kick in the teeth is an understatement for how we feel, how dejected we are.
"How much more difficult we've made our job today to survive in the Premier League is beyond what I can explain at the moment."
Southampton captain Jose Fonte was sent off for bundling over Fabio Borini when through on goal with 10 minutes to play in a low-quality battle on the south coast.
Second-half substitute Defoe duly exploited the extra space to prod home what he thought would prove the winner, only for Van Dijk to deny the Black Cats at the death.
Sunderland now face a fallow weekend before taking on relegation rivals Newcastle in the Tyne-Wear derby at St James' Park on Sunday, March 20.
Sunderland have left themselves open to being dragged into the relegation zone next weekend, should either Newcastle or Swansea claim victory.
"Victory today would have taken us three points clear of the relegation zone for the first time since I've been here," said Allardyce.
"And no game next week meant that if any of the bottom three win they couldn't overtake us
That would have been massive from a confidence point of view for our players.
"Just when you're thinking about saying 'here we are lads, look how important one-nil wins are', we've gone and thrown it away again.
"We have been very good value for more points than we've gained in the last few games.
"We shouldn't have been rescuing a point against Crystal Palace but we did, we shouldn't have been losing against West Ham but we did.
"We've got to stop it, and we've got to stop it very quickly because there's only nine games left.
"We've only got 25 points from 29 games: that's not enough.
"We've thrown it away and put more and more pressure on ourselves, which in the end I hope we can handle."
Southampton boss Ronald Koeman hopes the dramatic equaliser can spur his men back to form after a disappointing slump.
Saints have now gone three matches without a win, with Koeman accepting Tuesday's 2-0 loss at Bournemouth dented collective confidence.
"It's strange that we played some of our best football in the last five minutes," said Koeman.
"And it was a great goal
But the first 85 minutes was disappointing.
"My question to the players was why did we show that spirit and belief in the last five minutes when I saw them struggling before that?
"It's difficult to explain, but maybe they are unsure about themselves after the last two results.
"At least we showed great character at one-nil down and 10 against 11.
"Maybe this goal, this moment will be the key for us from now until the end of the season, as we still fight to get into Europe."
Source : PA
Source: PA