He had grown disillusioned with his treatment by current national coach Steve McNamara but former England chief Smith has slammed Brough for showing the wrong attitude.
He said: “Danny has changed his mind on more than one occasion on which country he is playing for.
“What most people would be disappointed in is the statement he is not prepared to play second fiddle to anybody.
“That’s exactly why you wouldn’t pick him.
“Anybody should be really honoured and privileged to represent their country, and if they’re asked to sit behind somebody or compete with somebody, overcome them and show a great attitude – that’s what we’re after as coaches.
“Sometimes players don’t show the best attitude within an environment. You’d rather have a great attitude than a great player.
“What you also want is people who are prepared to fight for their positions.”