"This is but the first step in a very long line of appeals that Mr. Simpson has before him," Galanter said.
Galanter was trying to reach Simpson in prison but had not yet spoken to the former NFL hall-of-famer, actor and advertising pitchman.
"I'm extremely disappointed," added Malcolm LaVergne, another Simpson lawyer. "I thought we had a very strong appeal."
The court said all eight separate issues raised in the appeal were without merit.
Clark County District Attorney David Roger was not immediately available for comment on the ruling.
Separately, the court ordered the conviction of Simpson's co-defendant Clarence "C.J." Stewart to be reversed and a new trial held. Stewart's lawyers successfully contended that Simpson's notoriety had hurt Stewart's ability to get a fair trial.
Stewart's attorney Brent Bryson said he and Stewart were happy with the ruling.
"This is no disrespect to O.J., but O.J. kind of made his own bed over the years," Bryson said. "My guy was kind of taken along for the ride."
Bryson planned to meet with Clark County prosecutors to determine the next legal steps while trying to get Stewart released from prison.
Simpson, 63, is serving nine to 33 years at a state prison in Lovelock Correctional Center, 90 miles northeast of Reno. Stewart, 56, is serving 7 1/2 to 27 years in Northern Nevada Correctional Center, a medium-security prison in Carson City.
Both men were convicted of kidnapping, armed robbery, conspiracy and other crimes for what Simpson maintained was an attempt to retrieve stolen family photos and mementoes from memorabilia dealers.
The key issues in the former football star's appeal were the racial makeup of the jury and the conduct of Clark County District Court Judge Jackie Glass.
Simpson's lawyers argued that prosecutors improperly rejected two jurors because they were African American. But the court concluded that except for providing the race of the prospective jurors, the lawyers didn't offer any evidence of discrimination. Prosecutors gave race-neutral reasons for dismissing the jurors, the court said.
The court also said it reviewed 34 instances in which Simpson's lawyers alleged misconduct by Glass, then concluded most of the allegations consisted of warnings by Glass for lawyers to stop talking and sit down.
The court also noted both sides in the case had been admonished during the trial.
"Of the 23 volumes of appendices, covering over four weeks of trial, there is hardly a moment of the trial where numerous attorneys were not trying to speak over one another," the court said in its order.
A spokeswoman for the Clark County Court did not immediately return a call from the AP seeking comment from Glass.
Prosecutor Roger has called the trial contentious but fair, and the sentences just. He had urged the justices to deny the appeals of both men.
The Nevada Supreme Court, however, said the lower court abused its discretion when it denied a motion to separate the trials of Stewart and Simpson. That ruling "prejudiced Stewart by having a substantial and injurious effect on the verdict," the court said.
Galanter has characterized Simpson's conviction as prejudicial "payback" for his 1994 double-murder acquittal involving the 1994 slayings of his ex-wife, Nicole Brown Simpson, and her friend Ron Goldman in Los Angeles.
Stewart is a former Simpson golfing partner from North Las Vegas.
Four other men took plea deals in the Las Vegas robbery case and received probation after testifying for the prosecution.