You were not wrong or cheap and have nothing to feel bad about.
Challenges are now part of the legal ruleset. They are a tactical option available to bot players. And your goal is to win, you ought to be pulling out all the legal stops in pursuit of that goal. They aren't a cheap or cheesy move.
So it unfortunately sounds like your opponent was simply a poor sport. Part of playing a competitive game and having people not dislike you aftwards is being able to win graciously and lose with dignity.
So as far as I can see, you did the right thing, you outplayed him that game if this made you win, and he needs to avoid putting himself in that position next time if he doesn't want to get challenged.