The Oranje manager saw his tactical changes pay immediate dividends as Brobbey struck twice inside the opening 17 minutes to put the Dutch firmly in control.
Despite the convincing win, Koeman stressed that his side must continue improving, while singling out Brobbey for special praise, particularly for his movement and finishing in the opening goal.
"In that first goal was everything you want, we know that Brian is good at that," Koeman said.
"It starts with Bart Verbruggen, who puts him away well. And then we have a lot of speed and Brian is again in front of the goal. You can't make a more perfect goal, starting from the goalkeeper.
"Despite the 5-1 victory, you do see moments that if they start playing differently, it takes us too much time to recognise that, which meant we got into a little too much trouble before