Anastasiia managed to escape the humanitarian crisis in Ukraine, landing Monday at LAX with her daughter, Sasha ... and she tells our photog a harrowing account of what's going on in their hometown.

It's pretty grim ... Anastasiia says she was confined to a basement for the last 10 days, which is no place to raise a child, with the sounds of bombs exploding and guns firing ringing out day and night.

Even worse, Anastasiia says the advancing Russian forces are raping young girls in Kyiv ... and she says the invaders are also murdering Ukrainians.

You can see the emotion building up in Anastasiia as she gives a first-hand account of what life is like for her Ukrainian brothers and sisters stuck in a war zone ... and the dangers they face.

She's keeping it together and is clearly a strong woman ... but the rapes and murders are what tug at her emotion ... and she tears up telling us what she's seen as she holds her daughter.

Like most refugees, Anastasiia has no plan for what she'll do in America ... she hasn't had time to think about it ... but she wants to find a way to help those struggling to stay alive back home.

She says her husband is protecting the family home, where her parents are still sequestered, and she hopes he's still alive when she goes back to Ukraine.

Anastasiia isn't sure what the average American can do to stop the war, but she has a message for the Russians ... telling them to rise up against Vladimir Putin and overthrow the government, like the Ukrainians did in 2014 when they didn't like their leadership.

The revolt paved the way for Volodymyr Zelensky's presidency a few years later ... and Anastasiia says he's united the country like never before, and hopes the Russians do the same.