The hosts had the majority of the ball for much of the encounter at St Mary's Stadium, but fell behind against the run of play after Juan Cala's 20-yard effort in the 65th minute.
And Pochettino, who saw Gaston Ramirez hit the crossbar in the first half, felt his side lacked cutting edge, wasting numerous opportunites to break the deadlock.
"We created plenty of chances, but weren't able to finalise them, and they scored from one chance they had on goal," he said.
"Lots of possession is useless if you don't actually make use of it and that was what happened today.
"We were not aggressive enough - we were moving forward and creating chances, but we weren't clinical enough in front of goal.
"We played our way - the same way that we have throughout the season. It was just that we lacked efficiency in front of goal."
Southampton had little to play for and the result sees them remain eighth in the top flight.
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