In a 5-4 ruling, the court said the use of midazolam in executions does not violate the ban on "cruel and unusual punishment."
"We have to stop executions until there's been a full investigation, independent investigation and full transparency," one lawyer said.
The execution of Clayton Lockett did not go off without a hitch Tuesday night.
Instead of death by lethal injection, the Oklahoman inmate died of a heart attack, with the complication attributed to vein failure, the Associated Press reported. The state corrections department was using a new three-drug combination, and the botched execution led them to postpone the execution of Charles F. Warner, also scheduled for Tuesday night, for two weeks.