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 this 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. 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 we started to play the same way that we did all through the second half on Wednesday."