The Dutchman scored an own goal to give the Gunners the lead 11 minutes into the game, and was substituted less than 20 minutes later, after sustaining a calf problem.
Nigel Adkins' men went on to lose the match 6-1, a defeat that has kept the newly-promoted Saints rooted to the foot of the Premier League. Still the former Heerenveen and Celtic defender is confident he can make a quick return and help Southampton earn their first points of the campaign.
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"First you get an own goal and then you can't continue the game so you can't set anything straight, but I'm working very hard on my rehab to make sure I get back as soon as possible.
"It was disappointing, but it's something you have to get over. It happened but we can't do anything about it, so it's onto the next one.
"We have to man up and get a smile back on our faces so we can enjoy our football."