If you have acquired the experience, by all means, mention it. You've earned the right to mention it. When it comes to management experience, nobody is too particular about where you got it from, as long as it is legit and you can talk about it as if you learned something valuable about it.
Management is anything but genius work and in fact, it's not supposed to be genius work. Because if management were genius work, we'd all be in serious trouble since maybe 1 in 1000 people is a genius, and that's too few geniuses for our management needs. Having said that, good managers who actually get things done are still hard to find.