The Celtics were tagged with six technical fouls during the 88-71 defeat and Rivers and forward Kevin Garnett were ejected. Nate Robinson and Kendrick Perkins also registered technicals after a fourth-quarter dust-up between Garnett and Phoenix's Channing Frye.
With the Celtics trailing 40-25, Rivers was ejected late in the second quarter after arguing with referee Steve Javie during a timeout. Rivers was hit with one technical foul and kept arguing with Javie, pointing to the official and his head as he yelled across the court.
Rivers could be seen on the broadcast chastising Javie, repeating, "It's all about you," and his mock clapping after the first technical led to Rivers' second infraction and his early departure.
"I just told my last son [Spencer, a high school freshman] that's he's going to have to get a scholarship," joked Rivers. "The other three [children, Jeremiah, Callie, and Austin] did, so he's just going to have to get to work."
Turning more serious, Rivers said he wasn't surprised by the fine and even acknowledged he didn't depart in a timely manner. But he doesn't know what constitutes a timely manner and proposed a gimmick for the NBA to adopt after ejections.
"My proposal is: Give us a 30-second clock," said Rivers. "When a coach gets thrown out of the game, they should start the clock and give you 30 seconds to vent. That would be terrific. I think the crowd would get into that."
Rivers said he ultimately has no problem with the fine.
"The low numbers tells you they didn't think it was anything awful," he said. "So I'm good with it."
Rivers said he thought Garnett should appeal the technicals, but said his player might simply be beyond the issue at this point.
Rivers also sounded off about the notion that Garnett took a cheap low blow at Frye, who got tapped below the belt while following through on an errant 3-point attempt.
"Watch the game tonight, you'll see 10 guys poked in the stomach [being boxed out]," said Rivers. "A guy jumps and it hits you in wrong place -- it just happens, it's not a big deal."
Information from ESPNBoston.com's Chris Forsberg was used in this report.