The Dark Blues were never at the races as the Lions won courtesy of a Bruce Anderson double at the start of the second half.
McPake accused some of his senior players of failing to pull their weight and concedes both he and the team are fighting for survival after falling five points adrift of safety.
McPake said: "The goals we lost were criminal at any level. Livingston are a good side and deserved to win.
"There are individuals who've played themselves out of the team, absolutely.
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