The win moves Southampton seven points clear of the relegation places but Pochettino refused to be drawn on whether his side might now be safe.
"I don't really know," he said. "What I am really focused on is preparing well for the next game against Chelsea and getting the three points.
"We played well today but I think the result made it seem like we have played better than we have in previous games.
"We have lost games when the team has played as well as they have done today.
"In football it is really important to be effective.
"Today we had a lot of goalscoring chances. We scored three goals, two more than Liverpool, and that led us to victory.
"I always like to get victories playing under our philosophy."