What the Earth used to be

A bird flew across a barren wasteland
Smoke rose in the air like a stirring dragon
A few creatures had survived
And they scuttled about
Their ribs protruded painfully
The bird continued its journey
Those pitiful mammals weren't worth eating
A few feathers fell onto the dusty plains
Next to a dried up riverbed
Which simmered like a dying snake
The bird kept flying on aching wings
It had a journey to find some place of green
Which smelled as sweet as possible
Even a patch of grass would do
Where it could rest its head
And die
Remembering for a fleeting moment
What the Earth used to be

Solid idea, nice work. The main weaknesses were in your tendency to over-write. You overused adjectives in a lot of parts, and this weakens the impact of your other words by crowding them, and telling the reader how to feel. Adjectives are primarily telling words.

A bird flew across a barren wasteland

Really, wasteland speaks for itself. It's a very powerful word on its own and by using another word to describe it you're cluttering that power.

Their ribs protruded painfully

Again, the adverb isn't necessary.

Those pitiful mammals weren't worth eating
A few feathers fell onto the dusty plains

Show us the mammals are pitiful. "Dusty" isn't really needed as in the next line you talk about the riverbed.
So basically question all the adjectives/adverbs you have and you'll have a much stronger piece. You use really good verbs and nouns so you don't need to overwrite.
I would also add punctuation which would really really help the flow of the poem. At the moment it tends to ramble and punctuation will let it breathe.

I think, if you actually chose a species of bird, this would automatically make the poem nicer and give a fuller depth of the poem. So choose a species of bird! You'll be glad you did.

It's very depressing, but I like the overall style of it, if that makes any sense. And the last line is the best out of the whole poem. I feel some spots didn't quite work, but that's already been pointed out. Also, even if you don't explain the species of bird, at least describe it. It'll make it so much more visually appealing to the reader