I conducted a Kruskal-Wallis test and the results were statistically significant. However, after conducting posthoc tests and calculating adjusted p-values for the test of mean difference between groups, none of these were statistically significant. Can I report that I found statistically significant differences but that I cannot say where the differences are? What would be the preferred way to report these results?
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You have the right idea for reporting: you will say that the global test for mean rank difference was statistically significant but none of the pairwise tests of mean rank difference were statistically significant after controlling for multiple testing. These results indicate one of two possibilities: either the global test was a false positive finding or the post hoc tests lack power.