Luis Suarez opened the scoring early in the first half at St Mary's and, having withstood the hosts' impressive response, Liverpool went out of sight thanks to goals from Raheem Sterling and Steven Gerrard.
Pochettino said: "We created many chances in the first half and we deserved a lot more from that first half and it should have been a different result.
"But we needed to be more clinical in the first half to get a different result going into the end of the half.
"We were unlucky not to score and then Sterling came on and with his first touch it was 2-0, and it was very difficult from then on to kick on and keep pushing.
"I thought overall with the team's performance it was an unfair result, but I do have to say Liverpool were a lot more clinical than we were."
- Sports & Recreation
- Raheem Sterling