The preposition "at" or "in" changes the meaning a little bit.  Here is how:

---

I am very bad in poetry
---

This is unusual.  This could mean:

>*I behave very badly* in *poetry class*.

But the listener should understand that "poetry" means **"poetry class"**, otherwise this is very unnatural.  Because this is such a specific situation, there would need to be **context**:

>"When do you find it hard to sit still and behave?" said the teacher.
>
>"I talk too much during music class," said Alice.
>
>"I misbehave during French class," said Bob.
>
>"I'm very bad in poetry," said Carol.

@Jason Bassford suggests it could also mean:

>*When I am portrayed in a poem*, I am *described as a very bad person*.

>"When songs and stories are told about me, they make me look like a hero," said Odysseus.
>
>"I am bad in poetry," said the minotaur.

Either of the above is pretty obscure.


---

I am very bad at poetry
---

This is very well understood to mean:

>I am very bad at **the art of** poetry.
>
>I am very bad at **the art of writing** poetry.
>
>I am very bad at **writing** poetry.
>
>I am very bad at **creating** poetry.

The use of "at" is so common in this kind of sentence, that "writing", "creating", or "the art of" --- all meaning **creating** --- can be dropped with no loss of meaning.

Dropping the participle is a little tricky, and just as in the first example, it requires **context**.   

Here, you can drop "creating" because poetry is an art, so we assume you mean **creating** the art, not **consuming** (reading or reciting) it, or **doing other things** (publishing it, copying it from books, lifting books of it, engraving it in stone).   This is generally understood. 

For any other usage besides the most common, you would need to *set the context* before dropping the word "creating".

> "What kind of text can you engrave?" said Alice the stonemason.
>
> **"I'm very bad at poetry,"** said Bob the engraver.
>
> "Me too," said Carol.

Some situations don't have **any** general understanding of what you mean. 
For example, this converation by itself is confusing:

> **"I'm very bad at furniture,"** said Alice.
>
> "Me too," said Bob.

But if you know this conversation is between two **woodworkers**, or two **painters**, or two **students studying the art of painting**, then you'll understand that they mean *building furniture*, *painting furniture*, or *painting pictures with furniture in them*.   

Dropping the "action word" -- the participle -- requires context for the situation to make sense.  **It's only safe to drop the action word when the context is obvious.**