The bill's author, Sen. Ed Murray, a New Orleans Democrat, noted that the drink was created in his hometown and has become world famous. But Sen. Buddy Shaw and others said it was inappropriate to honor an alcoholic beverage.
"Is there a possibility that we could be encouraging folks, who were not intending to drink, that it would be acceptable and they could become an alcoholic?" Shaw asked.
"No," Murray replied.
Three other senators who spoke in opposition said the passing the bill would "send the wrong message" about the state.
The legislation failed by a vote of 27-8. Five of its supporters represent the New Orleans area.
A Sazerac contains whiskey, sugar, bitters and absinthe, or a substitute anise-flavored liquor.