Stevenson told Dallas TV station KDFW he was in the parking lot looking for his phone after doing some celebrating at a friend's apartment.
"A couple cops came up to me, asked me was I drunk," Stevenson said. "I said no but I had a couple drinks. I guess he talked to somebody else and then he just put me in handcuffs for no reason."
He was arrested without incident on a Class C misdemeanor charge, based on the results of a sobriety test, an officer's observations and his statements.
"They felt he was a danger to himself and others," Irving public information officer John Argumaniz said. "Basically, he was intoxicated to a point where [police] didn't feel comfortable letting him walk away or leave. They didn't have any other options at that point."
Stevenson was released on $475 bond at 5:30 a.m. local time Wednesday.
In the interview with KDFW, Stevenson said the police characterization of his condition wasn't accurate.
"I always knew where I was at. ... If it was that bad, if it was that wasted, I wouldn't have been out of jail in three hours on a $400 fine," he said. "I just think people, they take things out of proportion, and when you're a champion everything is under a microscope."
The Mavericks said they were not aware of the incident and declined comment.
"I slept in a one-room cell for almost five hours, until my wife came and picked me up, and to me it hurts because that's not a way a champion should celebrate on his way home in Dallas, sleeping in a cell over a $400 fine," Stevenson told KDFW.
Stevenson, who will be a free agent July 1, is a rugged role player praised by teammates and coaches for his professionalism after bouncing in and out of the starting lineup all season.
Stevenson started throughout the playoffs until coach Rick Carlisle opted to replace him with J.J. Barea in Game 4 of the NBA Finals.
Stevenson still played a key role in the series, averaging 7.0 points in 17.2 minutes while making 13-of-23 attempts from 3-point range and playing excellent defense on Miami superstars Dwyane Wade and LeBron James.
Stevenson drew attention during the Finals for making critical comments about James, with whom he has feuded since they battled in the Washington Wizards-Cleveland Cavaliers playoff series from 2006 to 2008. Stevenson called the Heat "classless" after the Mavericks clinched the title. He had said James "checked out" in Game 4.
Tim MacMahon is a reporter and columnist for ESPNDallas.com.