Should "dews" be "dew" here? Can plural form dews stand?

is it part of a poem?

Not. Just a common sentence.

It isn't a sentence.

Yes, it is!
Flowers cried at night, and dews on leaves were left.

Dew can be both countable and non-countable. Non countable dew is moisture condensed from the air, but there are plenty of situations where dews in the plural would be appropriate, for example where a number of leaves are being considered as a collection of individual item, each with its own instance of dew.

Whoa buddy!! It's not common here and if it's not bad poetry then it's a really bad sentence.
You might say:
Flowers cried at night, the dew was like tears on the leaves.
or
Flowers cried at night, when dew was left on the leaves.
or
Flowers cried at night as dew on leaves was left. (more poetic, I guess)

I am a mighty oak; full two hundred years have I stood in the forest. My bark has been warmed by many dawns and my leaves have felt many dews.

(c) Contrex 2012