The 1-0 win at Swansea City means it is now six consecutive matches in which the opposition have failed to score against Ronald Koeman's side.
The club’s top-flight record is seven successive league matches – a mark Saints can now tie when they host Chelsea later this month – while their all-time best is eight.
But van Dijk says that is not on the players’ minds.
"Not about the record, personally. But it's always a very nice feeling for the defenders and for the whole team to keep a clean sheet, because we also have a lot of quality up front, so we always score a goal as well. At the moment it's been very good and hopefully we will keep going,” he told youtube.com/southamptonfc
Saints’ latest clean sheet rarely looked under threat at the Liberty Stadium, and van Dijk believes the defensive performance is something the whole team can be proud of.
"I think that's a big compliment for the whole team,” he said. “We must stay focused and keep doing the same things together. It's been great form that we are in right now and hopefully we can continue it.
"We will win as much as we can, with good football, and hopefully we can do it against Chelsea as well, but that's for another time.”