Gordon, a nine-time All-Star and five-time World Series winner with the New York Yankees and Cleveland Indians, was picked by a 12-member committee that only looked at players who started before 1943.
But a panel made up of the living 64 Hall of Famers failed to pick anyone who began their careers after World War II. It took 75 percent for election and no one came close -- Santo got 61 percent, followed by Jim Kaat, Tony Oliva, Hodges and Torre.
"When our board of directors restructured the Veterans Committee after the 2007 election, it did so with the goal of ensuring the voters the living Hall of Famers would review their peers," Hall chairman Jane Forbes Clark said. "The process was not redesigned with the goal of necessarily electing someone."
The results were announced at the baseball winter meetings in Las Vegas.
Gordon got 10 votes -- one more than needed -- and joined a host of past teammates in the Hall. He began his career with Lou Gehrig, Joe DiMaggio, Bill Dickey and other stars on the 1938 Yankees team that won the World Series, and finished with Bob Feller and more Cleveland luminaries in 1950.
Gordon was the 1942 AL MVP and hit .268 overall with 253 home runs and 975 RBIs, big power numbers for second basemen in that era. He died in 1978.
Pitcher Allie Reynolds, traded from Cleveland to the Yankees for Gordon after the 1946, fell one vote short of election.