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Hughes has stressed that he has no complaints with the way Blues handled the situation and he revealed that Savage was desperate to play in Baku, but was left at home because of a genuine groin injury.
"I've known Steve for many, many years and he understands what happens in football at times," Hughes said on BBC Wales Sport.
"It's not a good time for relations between the Welsh fans and Birmingham. But I think people need to understand that clubs have responsibilities towards their players and their own fans."
Hughes went on to condemn the Welsh fans who have conducted a hate campaign towards Bruce, forcing the Blues boss to change his phone number.
"That's not something anyone wants to encourage, it's an invasion of privacy, said the Wales boss.
"I think people's privacy should be respected. Obviously, feelings are running a little bit high at the moment, and people are reacting to that. To actually put someone's number on a website is irresponsible."
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