The oldest man on the pitch produced fine saves to deny Dani Osvaldo, Schneiderlin and Rickie Lambert, who also hit the post minutes into the second half.
Those missed chances almost allowed West Ham to snatch a late winner, only for the otherwise impressive James Collins to blaze over.
"We created the better chances, we were much closer than they were to actually getting a victory," the Argentinian said.
"But in football, it is not just about creating chances, you need to be make them into goals. We weren't able to do it and we are frustrated by that.
"I am pleased with all of my players - they all played well and put in a great effort.
"On the one hand, I am a bit frustrated because we didn't get the three points but I'm pleased, as they all played well."
Considering Southampton's abundance of attacking options, their lack of goals this campaign has been frustrating for Pochettino.
Osvaldo has yet to find the net since his club record move from Roma, while Lambert has yet to replicate the fine form he has shown for England.
"He has played the last two with national side, which must be a huge boost for his self-confidence," Pochettino said of Lambert.
"At the same time strikers need to score goals, that is their bread and butter.
"He hasn't been able to do that, none of them were able to do that, so I'm frustrated.
"We created many chances and on another day those chances might be goals."
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- Rickie Lambert