The visitors had just under 70 per cent possession in the 90 minutes and double the efforts at goal, but somehow still managed to be soundly beaten.
But Pochettino wasn't too disheartened, and took the positives from his side's display.
"I am very proud of the performance of the team," Pochettino told Sky Sports.
"There were certain situations that put the balance of the game in West Ham's favour, and that had a deciding effect on the game.
"It is clear that we created so many good chances and were unlucky not to take them.
"The result does not reflect on how we played, as we did quite well today."
With Saints cruising having taken an early lead, Matt Jarvis' levelled for the Hammers against the run of play and somewhat controversially having come from what seemed to be an offside position, a point Pochettino couldn't ignore.
"I don't believe it was offside, it can certify that it actually was offside," Pochettino added.
"It changed the course of the game completely.
"Overall we were quite unlucky with the refereeing decisions, as we also should have had a clear penalty."