"confession of weakness" is a correct and usable phrase in written English.
You can use it when you are wanting to admit to or express a vulnerability or lack of strength, either in yourself or in another person. For example: "I have made a confession of weakness: I am not sure that my research is good enough to get published."
The nomination has been hailed as a masterstroke, but it is also a confession of weakness.
"It is almost a confession of weakness to go into the media business.
Digging into Randy Newman's abject ballad, "Guilty," a substance abuser's groveling confession of weakness and failure, Ms. Dexter brings out its lurking subtext.
Indiana Democrats objected that the proclamation was "a confession of weakness — an acknowledgement that twenty millions of white people … can not conquer six millions of whites" without black help.
Jane wanted love, sexual and every kind; she said so all her life, and she was bold in saying so, because it is always taken as a confession of weakness.
The Hollywood mogul makes a rare confession of weakness: his greatest mistake, he said, was to have sold the company to the Japanese in 1990 a decision that ushered in a time of instability for Universal which continues to this day.
However, in its moral ambiguity, the hesitations of the hero and his confessions of weakness, lies its modernity, responding to the contemporary sense of moral sickness.
Perhaps you'd be surprised to know that it isn't the confessions of weakness that will hurt you but your inability to expose a keen sense of self-awareness.
The book includes a number of frank disclosures, including a confession of his weakness for alcohol.
To acknowledge Rawlins's importance, in McPherson's words again, was to make "a public confession of his own weaknesses".
Ernst's painting, too, is a confession of frailty, of the weakness of reason and selfhood in a mind that is only part conscious, part knowable.
