Brown's job is hanging by a thread after their defeat at Turf Moor on Saturday.
Coyle, who played alongside the then captain Brown at Bolton in the mid-1990s, said: "The last thing Browny will want is sympathy. He's a personal friend of mine. I'll see him now when I go back in.
"He was the captain at Bolton and has done a terrific job at Hull and again because he's raised the bar in terms of expectation that's the nature of the beast.
"Hull got into the Premier League and that's down to him being in charge and bringing them on.
"As I say they're not down and out they're right in the mix, but knowing him as I do he'll bounce back, he's a battler, he'll show his qualities."