The Clarets boss, who played alongside the then captain Brown at Bolton in the mid-1990s, believes his Hull counterpart has worked wonders during his three-year reign.
But a poor start to the season - with Hull lying 18th - has seen the Tigers boss come in for heavy criticism, and amidst growing speculation both the club and Brown himself have been forced to go on record insisting he remains in charge.
On Thursday morning the East Yorkshire side confirmed that club chairman, and a close friend of Brown's, Paul Duffen had resigned, raising further question marks about the Hull manager's future.
"Browny is a good friend of mine and was my captain at Bolton in a very successful team," said Coyle. "He is a man I've got a lot of time for. There's no doubt he's done a fantastic job at Hull but it's the nature of football that people are always on to you and are always critical."
He added: "I think the problem in football is that the more success you deliver then expectation rises. I've spoken about this before, balancing expectation and realism. That's what has happened at Hull. Taking them into the Premier League where they hadn't been raised the bar."