On Saturday, Eta became the first female coach to lead a Bundesliga team when she was appointed as interim coach at Union.
"I am actually really happy (with Eta's appointment)," Kompany told a press conference ahead of their Champions League return leg against Real Madrid on Wednesday.
"I think these are key moments. It is easy to minimise them and say 'she is just a coach like everybody else, and that is how we have to treat her as colleagues'.
"But in the end it is something special," the Belgian added.
"It opens a lot of opportunities to little girls who now play football and think 'I can coach anywhere, make a real career and be successful'. These stories are really important.
"I wish her all the best, and the only part I wish she is not treated like a man, is being patient with her, because the coaching job lacks patience on the leadership level."
The 34-year-old Eta had been coaching Union's Under-19 team and will take charge of the club's women's team from next season. She became the first female assistant coach in the German top flight with Union in 2023.
Union Berlin on Monday condemned sexist online abuse directed at Eta following her appointment, saying it was disappointing that the club had to respond to such criticism in 2026, calling the discourse "insane" and "embarrassing."