If I'm honest, the amount of fillers (I, the, but etc) you used throughout spoiled it for me and threw the flow in multiple places.
Maybe:

I am but a dead leaf
Floating through autumn skies
Searching below
For a cozy place to lay and die
Winds keep pushing
Leading me to world's edge
There are doubts
I've made my self pledge
Promised I will end
Laying in a field of self pity
With all the other leaves
All rotten, forgotten and shitty

"All rotten, forgotten and shitty"
^^I get the meaning here, and the feeling but the use of the word shitty makes it seem like you were just trying to continue with the rhyme scheme, and it makes it seemed forced. Reword maybe?

It does sting a bit
Realized the true meaning
Wind is no enemy
Though pain is demeaning
Wind is old
Means not to kill you
Life is full of pain
Sadly this is the truth
Understand
Leafs dropped from trees
Won't go far
But let to drift in the misery
Won't crush on landing

"But let to drift in the misery"-let? left?

Love the closing line, very powerful.

However I was thrown that most of the poem had a fixed rhyme whereas the last few lines didn't.