Brown takes his Hull side to Burnley on Saturday after days of feverish speculation over his own future.
Betting was suspended on Brown becoming the latest manager to lose his job earlier this week with the club being forced to issue a statement to clarify Brown's future.
Coyle, who was a team-mate of Brown's during their time together at Bolton, believes the Tigers manager is a victim of his own success.
"I think the problem in football is the more you deliver success then expectation rises and it is getting that balance between expectation and realism," said Coyle.
"I think that is what has happened at Hull.
"Taking them into the Premier League, where they hadn't been before, raised the bar then people expect that to be an onward process and continuing, but to do that you obviously need the right funding and the right players.
"But if people had said a few years ago to the Hull fans that they would be a Premier League team and Phil Brown would be the man to lead them there and take them on everyone then would have been absolutely delighted.
"How that changes all of sudden is beyond me.
"He studies football, leaves no stone unturned how he goes about his job and there is no doubt he is the right man for job and he will continue I think to take Hull onwards and upwards."