Gary Graham was put to death by lethal injection after last minute moves by his lawyers failed.
He had been on death row for 19 years and maintained his innocence throughout.
The case has sparked impassioned debate about the death penalty and emerged as a presidential election issue after Texas governor and White House candidate George W Bush refused to allow clemency.
Mr Bush, under fire for more than 130 executions that have taken place in
Texas in the five years that he has been governor, said he backed
Graham's execution and believed that justice was being done
because he was guilty.
In a statement Mrs Robinson said: "I believe the execution of Mr Graham ran counter to widely accepted international principles and to the international community's expressed desire for the abolition of the death penalty."
Graham was sentenced for shooting dead a man in Houston when he was 17 years old, and therefore a juvenile.
"The overwhelming international consensus that the death penalty shall not apply to juvenile offenders stems from the recognition that young persons lack maturity and judgment and thus cannot be expected to be fully responsible for their actions," she said.
Journalist eyewitnesses said Graham had to be subdued and carried into the execution room. They said it was obvious from the way he looked he had put up a struggle.
He was covered in a sheet and restrained as he was laid down to die.
In a long, rambling and angry statement he said he wanted everyone to know that his death was state sanctioned murder.
And he said that his killing was part of the genocide of blacks in America.
He added, unless something was done, there would be another 100 years of this kind of lynching.
His murder, he said, had to be avenged.
He went on to say that he had been treated brutally in prison but maintained that "you can kill a revolutionary but not the revolution".
Witnesses Bianca Jagger, Jesse Jackson and Al Sharpton were said to be very emotional as the time for the execution came near.
Journalists said as the drugs went into his body he looked over at Reverend Jackson, then let out a slight groan and died.
Afterwards Jesse Jackson said he had wept openly at witnessing his first execution.
The family of Graham's victim Bobby Lambert also made a short statement saying that although they were sad for his family they felt that justice had been done.
Then his lawyers launched a civil suit against the pardons and parole board for refusing a reprieve. Outside the jail several protesters were arrested trying to break a police barricade.
Graham pleaded guilty to 10 aggravated robberies during a crime spree 19 years ago.
But he insists his week-long rampage of robbery, rape and theft did not include the fatal shooting of an Arizona man outside a Houston supermarket.