Hi Hwan Lee,
Your example "there's just not Asians at this park" makes more sense than the apples example. If this is what you heard, it's still not great English.
The construction "there's just not _any_ Asians at this park" is used a lot in casual conversation, but is still not technically grammatically correct; it should be "There just aren't any Asians at this park." Being used in this way, "just" = "simply".
To know exactly what the speaker means, you would need to know more about the conversation taking place. For example, if their friend had said "I think we're in a racist park," the speaker might be expressing: "I don't think the _park_ is racist. I just/simply think that we can't see any Asians here at the moment." Alternatively, the phrase could be an exclamation suggesting: "We have a huge Asian population in this area, but there just/simply aren't any Asians here at all. What's going on?" I hope that makes sense.