United have been far from convincing in Van Gaal's first season in charge and the Manchester club's grip on a top-four finish in the Premier League loosened on Saturday after they crashed to a 2-1 defeat at Swansea City.
The 13-time Premier League champions have lacked creativity and penetration for much of the season and Koeman has offered an insight into what may be hindering United's UEFA Champions League hopes.
Koeman, who worked as Van Gaal's assistant at Barcelona between 1998-2000 before the pair fell out at Ajax, believes the 63-year-old's demanding approach puts too much pressure on players.
"When you bring Van Gaal in the house, you bring in quality," Koeman is quoted as saying by The Mirror. "But you also bring in someone who thinks he knows everything. And that will cause clashes.
"There is a big difference between him and me as managers. I was his assistant at Barcelona after the World Cup in 1998. I learned a lot of things from him.
"But the way he handles his players is totally different from the way I work. I don't put as much pressure on the shoulder of players.
"When you have Van Gaal in charge, it is a fact that there is fear in his team. The players have a fear for mister Van Gaal. That is not always good."
