Thursday's application for a stay of execution was referred to the court by U.S. Supreme Court Justice Elena Kagan.
Irick and other death row inmates have been part of a lawsuit that seeks to block use of Tennessee's lethal injection mix, which contains the sedative midazolam.
Europe, which opposes the death penalty, has refused to sell more effective drugs to the US that have been traditionally used for executions.
At around 3 p.m. Thursday, he ordered his last meal - a "super deluxe combo", according to the Tennessean.
"I just want to say I'm really sorry".
Tennessee carried out the execution Thursday of a man condemned for the 1985 rape and murder of a 7-year-old girl, marking the first time the state has applied the death penalty since 2009.
The convict, 59-year-old Billy Irick, had spent more than 30 years on death row, and was put to death at the Riverbend Maximum Security Institution in Nashville, Department of Corrections spokeswoman Tylee Tracer said.
"Although the Midazolam may temporarily render Irick unconscious, the onset of pain and suffocation will rouse him". Critics of the drug's use in lethal injections question its effectiveness, blaming it for prolonged and apparently painful executions, including that of Dennis McGuire in OH and Clayton Lockett in Oklahoma. Since then, the state has endured legal challenges and difficulties finding execution drugs including its previous one, pentobarbital.
On Monday, the state Supreme Court also had refused to block Irick's execution, saying the lawsuit filed by inmates involving the execution drugs wasn't likely to succeed.
That case is continuing in a state appeals court. "... If the law permits this execution to go forward in spite of the horrific final minutes that Irick may well experience, then we have stopped being a civilized nation and accepted barbarism".
Federal public defender Kelley Henry said at trial that inmates were tortured to death, feeling like they were suffocating, drowning and utterly confused.
The only noted dissent was from U.S. Supreme Court Justice Sonia Sotomayor; the court's order did not specify how the other justices would have voted.
"I hope tonight's lawful execution in some way eases the heartache Paula's family has lived with and brings a degree of closure to a chapter of their lives that has been indescribably hard", Mr Slatery said in the statement.
The execution was the first in Tennessee since 2009.
Prior to the pope's emboldened stance against the death penalty, three Catholic bishops in Tennessee wrote Gov. Bill Haslam, telling him that "the death penalty contributes to the growing disrespect for human life".
A second concern in Irick's case, according to Robert Durham, Executive Director of the Death Penalty Information Center, was that Irick was mentally ill.