When people admit mistakes they tend to use the phrase "my bad". I found that it is an informal way in North America. Could anyone help me with a better alternative?
“my bad” is slang and very informal.
“I made a mistake” or “that was my mistake” is formal, and just “my mistake” is informal.
The point of all these variants is to take ownership of the mistake: it was mine, not yours.
If you want to avoid saying who made the mistake or it’s not relevant, use passive voice: “a mistake was made”.