The fear of losing money will cause regret when you win a bet.
Nope, it will only cause a regret when someone loses his/her bet. That is actually going to make them regret and fear more of losing money because they have actually lost it.
In my opinion, it is just an illusion that crosses someone's mind because they are unable to bear the loss when they lose. In fact, if he was able to think objectively, winning and losing are part of gambling, maybe this small win would not have happened.
It is certain that losing and winning are part of gambling and with that, we don't want ourselves to dealt with losses even more. But then, when the reality strucks. We have to accept the fact that fear is there because all of us experienced losing and that means losing money too because we're bettors. But somehow, you might be right that it could just be an illusion that comes to our minds even if we're confident that we will not lose. Anyway, the thing with all of these fears are natural to a human's brain and we have to counter it if we are feeling that fear again, overcoming it is the only way to avoid it.