"Justice was served," Fallin, a Republican, wrote in a monthly column. "The people of Oklahoma do not have blood on their hands."
Convicted murderer and rapist Clayton Lockett, 38, died of an apparent heart attack on April 29 some 43 minutes after the lethal drugs was first administered.
A prison report said the botched execution was largely due to a collapsed vein during the injection and that the needle was inserted in Lockett's groin instead of his arm after prison officials used a stun gun to restrain him.
Fallin said people needed to be reminded of Lockett's crimes, which included robbery, rape and murder in a 1999 crime spree.
Among his crimes were shooting a 19-year-old girl and then helping to bury her alive in a shallow grave, where she died.
President Barack Obama, a Democrat, and Republican Texas Governor Rick Perry, whose state executes more people than any other, both had similar lines on the Oklahoma execution, saying something went terribly wrong.
