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 Saturday's 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."
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."
Source: PA
Source: PA