The push for a Senate inquiry into how the Essendon supplements saga was handled has failed after the government and the opposition refused to support the independent review.

The decision has been labelled an "extraordinary betrayal" by independent Victorian senator John Madigan.

The Senate voting changes threaten crossbench seantors' seats including those held by Senator John Madigan, centre, Senator Leyonhjelm, Ricky Muir, Glenn Lazarus, Dio Wang and Senator Day. Credit:Alex Ellinghausen

Independent senators Glenn Lazarus, Nick Xenophon, Zhenya "Dio" Wang, Jacqui Lambie, Ricky Muir, Bob Day and David Leyonhjelm all backed the motion for the Australian Sports Anti-Doping Authority to be grilled over its handling of the Bombers' probe.

Madigan's formal motion failed late on Wednesday in the Senate. He has vowed to pursue other options.