Performance director Wotte made his comments on Twitter after 29-year-old midfielder Commons announced he had quit Scotland on the same day national team boss Gordon Strachan left him out of his squad for next month's World Cup qualifier in Croatia.
Brown told a number of newspapers: "There is nothing wrong with Kris' desire. He has come to a club such as Celtic and shown what he can do. Kris trains hard, he's always in the gym. He is one of the first ones into training in the morning and one of the last ones to leave, so there is nothing wrong with his desire whatsoever."
Wotte had said: "Retiring at 29 after only 10 caps honestly still puzzles me. Where does pride, desire and ambition come into this picture? Agree?"
Commons who has a wife and three children, cited family reasons as one of the major motivations behind his decision.
"Every man to his own," said Brown. "We stay away in a lot of hotels on European trips and it is hard to see your family so I understand where he is coming from.
"We're also in a hotel for every match and you can sometimes be there three times a week.
"Then you have the three matches so you could be having just a night or two a week in your own house. It can be hard."
- Sports & Recreation
- Gordon Strachan