You could also say:
3. I've made the mistake of cursing people in this chat room.
4. I've made a mistake cursing people in this chat room.
5. I made a mistake when I cursed the people in this chat room. (Use the simple past.)
1. could mean that you intended to curse them, that you still have that intent; but that in cursing, you used the wrong words, or you weren't abusive enough ...
2. This implies that cursing them was a mistake.
3. This means you've made a common mistake - that of cursing people ...
4. and 5. These could mean any of them.
I think 2. is closest to your meaning, if you now believe it was a mistake to curse them. But the context in which you intend to produce this sentence would decide that.
If you intend this as part of an apology, the simple past with a time frame would be best.
I made a mistake last night when I cursed the people in this chat room. I want to apologise for that.
Student or Learner