The phrase "he bemoaned that" is correct and usable in written English.
You can use it to refer to someone expressing regret or sorrow about a particular situation. For example, "He bemoaned that he was the only one in his family who had failed to get a college degree."
He bemoaned that the current tax code was "incentivizing people to cohabitate instead of marry".
In the pessimistic book, he bemoaned that birthrate trends and "Third World" immigration were precipitating "the end of white America".
"What connects the strings to the people, that's the idea," he said, and then he bemoaned that in Lebanon, "there are so many strings".
He bemoaned that "we're living a tale of two cities," denounced the mayor's "ill-gotten gains" (the third term) and insisted that he had "stood up" to Bloomberg.
Espanyol's manager was sent off for calling the referee an hijo de puta, a son of a bitch, prompting a fabulously foul-mouthed post match press conference in which he bemoaned that the referee had gone for the obvious target.
He bemoaned that it took until now to get an Ebola vaccine ― one that is still unlicensed ― given the identification of Ebola as a top bioterrorism threat following Sept. 11.
Bolivia, among the poorest, most exploited nations, desperately needs export cash, Morales said, though he bemoans that need.
He bemoans that National Institute for Health and Clinical Excellence guidelines on sex education for young people have gathered dust on education secretary Michael Gove's desk since 2010.
In another segment, he bemoans that no matter your party affiliation, your politician of choice is going to let you down eventually, and your feeble attempts to defend his or her actions will fail.
Allsopp agreed, but bemoaned that "nature is not with you and I. Nature is not a feminist".
He only bemoaned that the Palestinian Authority hadn't done more to explain the import of its new U.N. status to the people.
