Coach Ronald Koeman said he was delighted with the performances of the pair in games against Bosnia and Germany, tempering concerns about who might step in for Memphis Depay if the 30-year-old's club future remained uncertain.
Depay, second on the list of the Netherlands’ all-time scorers with 46 goals in 98 appearances, has since signed for Brazilian club Corinthians and will likely be back in contention for the Dutch once match fit.
Zirkzee, who signed for Manchester United in July, scored in his first start for the national team on Saturday when the Dutch opened their Nations League campaign with a 5-2 win over Bosnia in Eindhoven.
Ajax striker Brobbey got his chance to prove himself against Germany and proved a real handful for their defence in Tuesday's 2-2 draw in Amsterdam, with his marker Jonathan Tah taken off at half-time.
"Tah was not substituted for nothing," said Koeman. "He pulled Brobbey’s shirt five times and committed a foul each time. Brobbey held him off very well.
"The second goal also came from Brobbey. I am super satisfied with him. He got his chance, and it was great that he took it like that. I am glad I chose him. He is fast and strong."
Zirkzee did not get a run out on Tuesday but was also praised by Koeman, who had announced beforehand that Zirkzee would start the first game and Brobbey the second.
"Joshua is strong and together with Tijjani Reijnders they formed a good team," said Koeman on Saturday.