Hayen was dismissed on December 8 after Club Brugge slipped to third in the Belgian league, some 48 hours before they hosted Arsenal in a move Garcia labelled "incomprehensible and unfair".
"It's illogical to dismiss a manager who has achieved great things, who made his team play well, and who achieved results in the Champions League," Garcia said at a press conference on Thursday.
"We need Belgian managers like him. But I'm not a club president, so in my case it's a matter of solidarity as a manager. I don't like it when managers are simply replaced."
But the Belgian football federation moved swiftly to avoid any potential conflict with one of the country’s biggest clubs.
"It is reiterated that such a decision rests exclusively with the parties concerned and that this was an internal club matter, as in other similar situations,” said spokesperson David Steegen about the sacking.
“The federation believes it is appropriate to focus on its own operations and ambitions."