Veteran goalkeeper Jussi Jaaskelainen was in fine form for West Ham at St Mary's Stadium as he denied the likes of Pablo Daniel Osvaldo and Morgan Schneiderlin with a string of fine saves.
Rickie Lambert also hit the post as Southampton were left to rue what could have been.
Pochettino's men have won just one of their first four Premier League games, but the Argentinian preferred to remain positive after the stalemate against Sam Allardyce's side.
"Yes, we created the better chances and we were much closer than they were to actually getting the victory," said Pochettino.
"But in football it is not just about creating chances, you actually have to make those chances be goals. We weren't able to do it and we are frustrated about that.
"I am pleased with all of my players, I think that they all played very well, I think they all put in a great effort.
"On the one hand I am a little bit frustrated because we didn’t get the three points, but at the same time, I am pleased because I saw that my players all played very well."
Pochettino also played down Lambert's failure to find the net against West Ham on his 200th appearance for the club.
The 31-year-old started for England in recent FIFA World Cup qualifiers against Moldova and Ukraine, scoring against the former, and Pochettino refused to dwell on his performance.
He added: "He has played the last two games with his national side and that must be a huge boost for his self-confidence but at the same time strikers need to score goals.
"It is their bread and butter basically and he has not been able to do that (against West Ham), none of my players have been able to do that and I am frustrated about that but overall we are pleased because we created many good chances.
"I’m pretty sure that those chances in the future will actually be goals."
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