Captain Gary Caldwell put the Latics ahead in the 25th minute but Saints dominated more and more as the match went on and thoroughly deserved their 64th-minute equaliser through Rickie Lambert.
The visitors thought they had won it when Morgan Schneiderlin ended an 85th-minute break by smashing past Ali Al Habsi but Shaun Maloney popped up in the 90th minute to prod in an equaliser.
Since replacing Nigel Adkins, Pochettino has overseen a draw against Everton, a narrow defeat by Manchester United and the point, but Saints have arguably been the better side in all three matches.
The Argentinian said: "I am frustrated, the same as the rest of the boys, because the team played a great match. The effort that the team put in, they deserved the victory today. It could be two victories and one draw.
"That's football. Sometimes you have luck and sometimes you don't have luck. But you have to work to produce your own luck.
"At Old Trafford we had two very different halves, raising our game a lot in the second half. I think in the last 10 minutes of the first half today we started to play the same way that we did all through the second half on Wednesday."
After good chances for Franco Di Santo and Gaston Ramirez, Wigan took the lead when Caldwell headed in a Jean Beausejour corner.
There was almost a bizarre leveller straight away as James McCarthy's clearance hit Schneiderlin and would have found the top corner but for Al Habsi.
Wigan held on until half-time but they were increasingly under the cosh and it was no surprise when Lambert levelled, beating Al Habsi to a header, while substitute Adam Lallana hit a post.
They looked like they had got their just rewards five minutes from time when Jay Rodriguez broke away down the left from a Wigan corner and crossed for Schneiderlin.
But the Latics had the final say, and it was defender Paul Scharner, who arrived back at the club on loan from Hamburg this week, who set it up with a header from a corner that was scuffed in by Maloney.
Wigan boss Roberto Martinez was a relieved man, although his club are now two points from safety after Reading continued their fine run with victory over Sunderland.
The Spaniard said: "You have to be (relieved) because Southampton got a very good momentum in the second half and when they get the second goal that late in the game it's going to be very difficult not to be affected by dropping points that you felt you had.
"I was very pleased with the reaction we had, the character and the desire to want to get a positive result, so in that respect I'm very pleased, even though I don't think we performed in the manner we want to or with the fluency we normally have.
"Scoring the first goal should give you a confident feeling but you could feel the crowd was getting very anxious and all of a sudden it became an exercise of something to lose rather than something to gain.
"We wanted the game to end then, and the way we finished the first half reflected that.
"Southampton pressed us really well, I think they're a very well-drilled team and they deserve huge credit but obviously from our point of view we need to understand that getting a goal lead should be something we can use in our favour.
"But we never accepted defeat and I think we got a very positive result. We managed to rescue a point and that could be very important at the end of the season."
Southampton are three points ahead of Wigan and Aston Villa but Pochettino does not yet want to think about his side's chances of staying up.
He said: "It's far too early to start talking about these problems yet. We will carry on in the same way and we'll see. I think this team is good enough for this league. I'm happy but day by day I'll ask for a little bit more."