The 26-year-old, who swapped clubs last month in a record transfer for a defender, played the full 90 minutes of the Reds' triumph on the south coast on Sunday afternoon.
Having silenced the St Mary's boo-boys with a solid performance, Van Dijk - a Southampton player for two-and-a-half years before departing in January - insists that it was business as usual from a personal point of view.
"I enjoyed it a lot. I just focused on the game, I enjoyed being back, I had a lot of good memories and a lot of good things I did here," he told Sky Sports News.
"Unfortunately they're not in a good position right now, but as a Liverpool player I was very happy with the win. I can't do anything about the reception, I just did what I could."
Van Dijk had failed to keep a clean sheet in his previous four Liverpool appearances prior to Sunday's match.