How to query entities/nodes that does not have the field "field_parent" with EntityFieldQuery?
You can't (natively) I'm afraid. An EntityFieldQuery doesn't have support for IS NULL or IS NOT NULL.

There are workarounds, however, essentially by adding a tag to the query and implementing a query alter hook, in which you add the required LEFT JOIN and IS NULL statement.

See EntityFieldQuery does not support isNull or isNotNull for a code example. I've used that code before with good results.