The phrase "an embarrassing level of" is correct and usable in written English.
It can be used to describe a degree or extent of something that is considered shameful or awkward.
Example: "The report revealed an embarrassing level of mismanagement within the organization."
Alternatives: "a shameful degree of" or "a humiliating amount of".
Carolyn Christhe-Bakargiev, the curator of Ms. Cardiff's P.S. 1 show, described the voice as a "point of surrender" bordering on an almost embarrassing level of intimacy between viewer and artist.
On a purely skin-deep level, both Jaguars prompted an almost embarrassing level of compliments and admiration during my test drives.
"While I can't speak for God, I have to say the electorate in my own back yard spoke last night and it was an almost embarrassing level of endorsement and I am very, very grateful to them".
Throughout the 80's and 90's we became international laughing stocks by cutting military spending to an embarrassing level, even risking the safety of our soldiers by equipping them with outdated gear in the process (something that dangerously continued into the Afghan War).
His weight climbed to an embarrassing level, and he kept thinking that his father had died of a heart attack at 56.
The rhetorical battle between the Executive Branch and the Legislative Branch appears to be diluting the well-intentioned goal of ending the embarrassing level of state corruption, and the legislative battle over the commission's subpoena practice is draining sorely needed state funds.
The right-wing tabloid Daily Mails critic wrote that the episode "veered a little too close last night towards the category of 'adult entertainment', with all its connotations of sleaze and smut" and "we found ourselves immersed in their sex lives on a level of embarrassing intimacy which most people would share only with their doctor".
Some imperative sociocultural maneuvering was missed when Girls debuted; instead, a really embarrassing junior-kindergarten level of communal reinforcement led to the collective conclusion that Lena Dunham's show is racist (and, yeah, that communally reinforced idea was right, because that show is racist to the point of making Brooklyn look like a sundown town).
