BRUSSELS—The European Union’s law-and-order mission in Kosovo didn’t attempt to cover up allegations of corruption in its own ranks, but its handling of the accusations has damaged the credibility of the bloc’s largest civilian operation outside the EU, according to an expert report.

The report, commissioned by the EU’s foreign-policy chief, Federica Mogherini, and presented on Tuesday, revealed shortcomings in the way the mission conducted an investigation into the allegations and communicated them both internally and to...