Goals from Morgan Schneiderlin, Rickie Lambert and Jay Rodriguez provided Pochettino with his second victory as manager and lifted Southampton seven points away from the relegation zone.
Pochettino was pleased with how his players responded to Liverpool pulling a goal back before half-time and feels three points were coming.
"I'm very pleased," Pochettino, speaking through an interpreter, told Sky Sports. "In the first half we played a very good game and we had many, many chances to actually go 4-0 or 5-0 ahead.
"We were fully focused on the game. My team believed and we had the correct mentality to compete well today. We prepared really well for this game and we fully deserved this victory.
"My team followed the same mentality, the same philosophy and same outlook. In the second half, they took control of the game for a bit but I think overall we dominated after that and had even more chances to increase our lead.
"We were a lot more effective in terms of scoring. We maintained our shape, we maintained our outlook and I think in all these matches we followed the same trajectory. It was overdue that we were going to get a victory like this today."
Pochettino is refusing to set a points target for safety and is merely focusing on the next game against Chelsea in two weeks' time.
He added: "The most important thing is getting the three points against Chelsea. The most important thing we need to focus on is fully preparing for the next game."