Robert K. Massie states that the four Grand Duchesses were quite cloistered at Tsarskoe Selo. It is known that the Olga, Titianna, Maria and Anastasia wore Rasputin's image on their necklaces. It is believed that to the Imperial Family believed he was the holiest of men.
We know that Nicholas and Alexandra were aware of St. Petersburg society's hatred for Grigory Effimovitch Rasputin. Pavel, a son of the Tsar's uncle, took a leading role in the mad monk's murder. This must have been quite a shock to the young Anastasia, who might have been unaware of any hatred towards the Imperial Family until that point.