Whatever one thinks about the wisdom of leaving, many flawed decisions by major policymakers paved the way for this result. Eurocrats upset at this result have mostly themselves to blame.
The pro-Remain side often made simply a negative case, focusing on how bad Leaving would be. Remain's "Project Fear" warned about economic disaster and moral disgrace if the UK left the EU. Remainers often attacked proponents of Leave as backward-looking nativists and isolationists. However, this tactic apparently came up short--which should be a reminder that the politics of shame can reach a point of diminishing returns.
The vote to Leave should not necessarily be seen as a turn toward radical isolationism. A reckless transnationalism is in many ways the enemy of a productive internationalism. The UK exiting the EU does create some international instabilities over the short term, but decisions made by many pro-EU forces on migration, trade, and other issues have likely increased instabilities much more. Some of the decisions made by EU leaders have perhaps increased the chances of the current international system breaking down.
The European Union is not Europe. Contrary to what many in the media seem to assume, an independent Britain can certainly enter into international negotiations with the rest of Europe.