Ten Hag is widely expected to be confirmed as the Red Devils' new boss in the coming weeks, leaving his role as Ajax Amsterdam manager at the end of this season.
United are currently under the tutelage of German tactician Ralph Rangnick but they face a fight to secure Champions League qualification for next season.
The Old Trafford outfit are currently seventh in the Premier League, six points behind Tottenham Hotspurs in fourth place.
Van der Vaart said on Ziggo Sport: "As a player you no longer have any arguments. Coaches have been sent away and they have a great squad, but they play really badly.
"It's not always the coach's fault. Now there will be a trainer who will be very clear.
"You can say: Ten Hag is not the big name in England. That may also be an advantage, because he is going to give his plan very clearly. If you don't cooperate, you will likely be thrown out."
Van Der Vaart also had a word of advice for Ten Hag not to keep United waiting, with Mauricio Pochettino also in the frame for the Old Trafford top job.
"You read reports that he is keeping Manchester United waiting," added the former Real Madrid man.
"If Ten Hag receives such an offer, he should not even think about it and go with that banana.
"That's an impression. You have to stay a little humble. He is a great trainer, he did a great job at Ajax. But Manchester United or the big clubs, don't let them wait."
