The defender wants the side to keep up the momentum after another disappointing second half display.
The Saints flew into the lead in the first half against the Cherries, but slackened in the second half to allow Eddie Howe’s side back into the game to dominate proceedings.
It is not the first time that the Saints have enjoyed a strong first half only to slacken and let their opponents back into the game in the second half, and Van Dijk says it is something they need to work on improving in future.
“That’s happened already a couple of times before and it’s something we need to work on,” he told saintsfc.co.uk
“We need to look at ourselves because I think we gave them the opportunity to come back and it gave them confidence I think. We need to do better and find a final solution to it.”
The win was a big result for Ronald Koeman’s side as they continued their fine run of form to sit seventh in the table.
They are now unbeaten in five games, with Van Dijk being a big part of that as he continues to impress in the heart of the defence since joining from Celtic in the summer.
Many are backing them to challenge for another top seven finish this season, and Van Dijk agrees, saying they need to keep going considering the quality they have in the team.
“I think (with) the quality we have in the team, we need to keep going,” he added.
“You can’t make mistakes really, otherwise you get punished for it and that’s a good thing. I’m enjoying every game playing against the best players in the world so it’s very good.”