Gillick received 13 votes from the 16-man Veterans Committee in totals announced Monday. Miller, the union head who revolutionized sports by gaining baseball players free agency and multimillion dollar salaries, got 11 -- one shy of the necessary 75 percent.
Steinbrenner, who left an indelible imprint on baseball as the New York Yankees colorful owner from 1973 until his death in July, received fewer than eight.
Miller, 93, appeared on the ballot for the fifth time and came the closest this year. Commissioner Bud Selig publicly favored Steinbrenner and Miller for election.
"The Marvin decision is stupefying," former Commissioner Fay Vincent said in an interview.
"A long time ago, it became apparent that the Hall sought to bury me long before my time, as a metaphor for burying the union and eradicating its real influence," Miller said in a statement.
Gillick was GM of Toronto, Baltimore, Seattle and Philadelphia, winning World Series titles with the Blue Jays in 1992 and 1993, and with the Phillies in 2008. He will be inducted July 24 along with any players chosen next month by the Baseball Writers' Association of America.