Goals from Luis Suarez, Raheem Sterling and Steven Gerrard fired Brendan Rodgers' men into second, leaving Saints with their fourth home defeat of the season
Goals from Luis Suarez, Raheem Sterling and Steven Gerrard fired Liverpool into second place, leaving Southampton with their fourth home defeat of the season.
"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," Pochettino 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.
"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."