Koeman said they were careless in possession of the ball while Van Dijk said the winning margin flattered them.
The Dutch started slowly and scored with their first shot on goal, a long-range effort in the 40th minute from Tijjani Reijnders at the Johan Cruyff Arena.
They had to weather many Scottish attacks before netting a second from Georginio Wijnaldum in the 72nd minute and then grabbing two more late goals from substitutes Wout Weghorst and Donyell Malen.
"It is, of course, strange that if you win 4-0 you are not satisfied, but that is the reality now. With the exception of the last phase, we were not good with the ball," said Koeman.
“We won’t win the European Championship playing like that,” was his cold assessment.
“The start was very restless and sloppy, against a team that kept causing us problems. When you make these kinds of mistakes in your build-up, give away so much possession, you will never grow in a match. That really needs to be much improved."
The Dutch were hit by injury and the match offered a chance for fringe players, like the Bundesliga-based Jeremie Frimpong and Xavi Simons to make a mark, but Koeman was not impressed.
"That could be due to a bit of pressure or wanting to do well and not having the confidence you play with every weekend," the coach added.
“Ultimately, the Dutch national team demands a certain level, regardless of your position or how often you are called up. They have that, but they have to play better.”
Van Dijk thought it was a tough encounter. “There are plenty of things that need to be improved if we want to do something at the European Championship," said the Dutch captain.
"If you look at the match, this is not really a 4-0 scoreline.”
The Dutch continue their preparations with a friendly against Euro 2024 hosts Germany in Frankfurt on Tuesday.
