The Southampton manager is highly critical of the way Man United handled Van Gaal's sack.
The duo are well respected within Dutch football settings but are fierce rivals and not best of friends.
Koeman, however thinks the way the United board handled Van Gaal's sack wasn't the best.
Months before Van Gaal's eventual sack, news and rumors of Mourinho becoming United's new manager had been circulating.
There were reports that United officials had clandestine meetings with the Mourinho camp, to make sure the former Chelsea manager didn't agree to a deal with another club.
News that Van Gaal will be sacked gained momentum, minutes after United won the FA Cup, and the Dutchman was sacked 48 hours later.
Koeman thinks his countryman wasn't fairly treated.
"I have watched the process around Louis van Gaal and Jose Mourinho from a distance. For months we were all reading that Mourinho was busy with Manchester United," The Southampton gaffer wrote in De Telegraaf via ESPN.
"If Louis was not told about getting the sack until after the FA Cup final, then Manchester United as a club don't deserve a medal for the way they treated him.
"If you know a little bit about the business at the highest level in football, then you know that these kind of deals are not done overnight. But Louis has been put under tremendous pressure for months. This is why I admire the way he kept his dignity."
Koeman believes there were moments when Van Gaal could have handled certain cases with the media in a much better way, but still praised the 64 year old for winning the FA Cup.
"Of course, he had a number of run-ins with the media and there were moments when I thought 'Louis, you could have dealt with that in another way.' But Louis is Louis. Looking at the incredible pressure all around him, I think he did a great job winning a big trophy like the FA Cup."
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