The visitors to Upton Park took the lead through Maya Yoshida after just eight minutes, but departed the capital with nothing as Matt Jarvis, Carlton Cole and Kevin Nolan scored for West Ham.
Pochettino, who saw his side spurn a host of chances, claimed the result was not a fair reflection of Southampton's performance.
He said: "I'm very disappointed with the result. I thought we definitetly deserved to get more from the game.
"We had full control and that even led us to get the one-nil (lead)."
West Ham's equaliser was a source of particular frustration for Pochettino, who insisted Jarvis should have been ruled offside before he chipped home.
"It's clear that the 1-1 (equaliser) came from an offfside position and that was unlucky for us and then the team struggled to recover from going 2-1 down. That made it quite difficult for us," he added.
"I thought in the second half we created many good chances to get to 2-2, which actually would have changed the game."
Pochettino was also unimpressed by the performance of referee Mark Clattenburg, who took charge of a Southampton match for the first time since being cleared of wrongdoing over comments he made to the club's England international Adam Lallana during a fixture against Everton in December.
However, the Argentinian reiterated his desire to move on from the incident.
"The refereeing decisions actually influenced the game today and we were unlucky in that sense," he added.
"We don't want to make anything more out of it. It seems the stars are not with us when Mr Clattenburg referees for us.
"I thought overall the team worked very well. We always knew that it was going to be a very tough game against very good opposition and I think what we lacked was exactly what they had, which was effectiveness."