"Could not believe that such a World War could break out as a result of an act like his. They did indeed think that such a World War might break out, but not at that moment."

From the 1916 notes of Dr. Pappenheim, a future collaborator with Sigmund Freud, who interviewed Princip in his cell in Terezin/Theresienstadt.

He regretted killing Sophie, Ferdinands's wife:

"His only sign of regret was the statement that he was sorry he had killed the wife of the Archduke. He had aimed only at her husband and would have preferred that any other bullet should have struck General Potiorek." - Borijove Jevtic, an associate of Princip.

However he initially showed little care for the consequences of his actions. He said in October 1914 "I am the son of peasants and I know what is happening in the villages. That is why I wanted to take revenge, and I regret nothing."

Later, in 1916, he spoke with Dr. Pappenheim and stated: “The World War would not have failed to come, independent of [the assassination].” See also the post by /u/indibidiguidibil.

According to Norman Stone, Princip is reported to have also said 'If I hadn't done it, the Germans would have found another excuse.'

In general, and according to various indirect quotes I am unable to verify, Princip did not feel regret so much as sadness that his shots had started the conflict.