Generally they say things like "well, that was sufficiently awkward," by which they mean that something was extremely awkward.
Now, there are instances in which things can be sufficiently awkward. But they must be sufficiently awkward to do something. The sufficiency must have some effect. Sufficiently hot to fry an egg. Sufficiently deep and wide to kill Mercutio. Sufficiently awkward to make me never want to return to the scene of the crime.
Otherwise you can just say "very." It won't be graceful, but it also won't be wrong.