Luis Suarez's opener ensured Pochettino's men went in a goal behind at the break at St Mary's Stadium despite creating a host of opportunities.
Suarez then laid on the second for substitute Raheem Sterling shortly before the hour and was fouled for a late penalty, which was duly converted by Steven Gerrard in the game's closing stages.
Pochettino lamented Southampton's inability to take their chances but insisted the result was unfair on his side.
"We created a lot of chances in the first half and we deserved a lot more from the half. It should have been a different result but we just have to be a lot more clinical in the first half to get a different result," he said.
"We were unlucky to score in the first half and then Sterling came on, (scores with) his first touch and it's 2-0.
"I thought overall with the team's performance it was an unfair result but Liverpool were a lot more clinical than we were."
Pochettino was undecided on whether Adam Lallana was deserving of a penalty after going to ground under the challenge of Jon Flanagan in the first half.
He also suggested a lack of luck hindered Southampton as they lost a third-straight game in all competitions.
On the penalty, he explained: "It could be. From my place on the pitch it was quite difficult to see. It could be a penalty.
"We were unlucky in many respects as we were unlucky in the last game (against West Ham).
"When you're not clinical against teams like Liverpool, it's always going to be difficult to get something positive out of the game."
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