Apostool focused on topographical accuracy and atmospheric depth. In works like Het dal van de Anio met de watervallen van Tivoli, he used subtle gradations of grey to suggest volume. His style avoided the dramatic flourishes of contemporary Romanticism. He preferred a controlled and observational approach. This is evident in De herberg Holland op 't Smalst. The composition relies on clear spatial divisions and structural clarity.

Collectors value Apostool for his ability to balance technical discipline with a quiet sense of place. His prints of European castles and mountainous scenery provide a window into nineteenth-century travel. This is seen in Bergachtig landschap in Spanje and Kasteel en bergachtig landschap. The neutral palettes and architectural focus make his work suitable for modern interiors. His prints offer a sense of historical documentation. They are both informative and visually calm.