His above-average intelligence let him engage a German elementary school in Tinjan and Pazin, then a gymnasium in Gorizia, and Karlovac where he also attended a seminary.
Dobrila studied with and was a friend of Josip Juraj Strossmayer, another Croatian bishop and benefactor of the 19th century.
He was a vocal supporter of the Croat and Slovene population in Istria, which was the majority there, but culturally and politically dominated by Italians from the coastal towns.
He supported the introduction of the Slavic languages into schools and public life, funded children who wanted to attend schools in the Croatian part of the monarchy (in Rijeka and Kastav) and encouraged the peasants in Istria, mostly composed of Slavic people, to read books in their native language and avoid being abused by their mostly Italian lords.
He was also a participant of the First Vatican Council (1870) where he supported Bishop Josip Juraj Strossmayer's opposition to the doctrine of papal infallibility.