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 the press. It also said that if the mission, known as Eulex, remained in Kosovo it needed to improve both its effectiveness and credibility.

“Set up to safeguard the rule of law, [Eulex] has been accused to of undermining that rule of law,” wrote Jean Paul Jacqué, the French law professor commissioned to draft the report. “Its credibility has been damaged to the point that its actions will henceforth often be tainted with suspicion and every decision to convict or not to convict will risk being criticized on the basis of corruption.”

Created after Kosovo declared independence from Serbia in 2008, Eulex was meant to help the new country build up a robust police force and judicial institutions to fight criminal networks and corruption. But it has come under fire both in Kosovo, where politicians have been unhappy with Eulex’s far-reaching power, and by outsiders questioning whether its achievements warranted its costs.

Since its launch, Eulex has cost more than €750 million ($794 million) and won fewer than 400 verdicts related to corruption, organized crime and war crimes.

Mr. Jacqué’s report revolves around allegations made in 2012 byMariah Bamieh, a then-prosecutor for Eulex. Ms. Bamieh, whose name was blacked out in Tuesday’s report but who has in the past spoken to the press, had alerted her superiors to a transcript of tapped phone conversations that she said pointed to serious corruption among Eulex judges and prosecutors.

In those phone calls, a Kosovar prisoner sought, through intermediaries, to contact Eulex judges and prosecutors to arrange his release and acquittal, but didn’t actually make reference to money being paid, Mr. Jacqué wrote in his report. Ms. Bamieh claimed her superiors didn’t pay sufficient heed to these allegations and subsequently punished her by first suspending and then refusing to rehire her. She couldn’t be reached for comment Tuesday.

Tuesday’s report didn’t examine the substance of the initial corruption allegations made by Ms. Bamieh. Those accusations are the subject of a separate investigation that has already led to the partial lifting of immunity for one Eulex official. Instead, it examined whether officials in Brussels or Pristina, Kosovo’s capital, had tried to cover up the allegations and treated Ms. Bamieh unfairly.

Mr. Jacqué, who in the past has worked for the EU, said he found no proof of a coverup and that the decisions to suspend and then not rehire Ms. Bamieh weren’t taken to punish her. He also said that she didn’t qualify as an external whistleblower—a status that would have given her special protection under EU law— because there was an internal follow-up to her allegations.

But the report found that her allegations should have been investigated from the start and that a lack of communication within Eulex, along with the short duration of many officials’ posting, had undermined the mission’s effectiveness and credibility.

“The continued presence of Eulex is only feasible if comprehensive reforms are made,” Mr. Jacqué wrote. “There is no point in staying just to keep doing the same thing.” Ms. Mogherini, who commissioned the report shortly after taking office in November, said her services were studying its findings and looking at the best ways of addressing Mr. Jacqué’s recommendations. A spokesman for Eulex didn’t respond to requests for comment.