There are several synonyms that can be used instead of the phrase "shameful incident." One option is "disgraceful event," which implies that the occurrence was not only shameful but also brought disgrace or disrepute to those involved. Another possible synonym is "embarrassing situation," which suggests that the event was awkward or uncomfortable for those involved and may have caused them embarrassment. "Scandalous incident" is another alternative that conveys the idea of a shameful occurrence that has caused outrage or scandal. Finally, "regrettable occurrence" is a more neutral synonym that suggests that the event was unfortunate or regrettable but does not necessarily carry the same sense of shame or disgrace.