Yeah, I also found that difference intriguing between Polish and Russian and got many Polish exercises wrong at first, thinking in Russian.
I don't have documentation, but it's like this: When there is none of something, the negation modifies the noun, and the noun case always takes the genitive.
Нет цветов у меня дома. Цветов нет тут. Нет там цветов.
But if the negation just modifies the verb, then the direct object doesn't need to be in genitive and just follows standard noun case rules.
Я не люблю цветы. Он ей не принёс цветы.
In Polish, it seems that the whole sentence "goes negative."