Boston's Ray Allen had his potential game-winning jumper in the closing seconds of the extra session altered by the Lakers' Pau Gasol and Derek Fisher, who appeared to hand-check Allen before his shot went awry, securing LA's victory.
Rivers also was angered because all-star forward Kevin Garnett had fouled out late in the fourth quarter.
"I thought in the third and fourth quarter the game got out of control," Rivers told the Boston Herald after the contest. "And I thought the officials allowed it to get out of control. I just thought there was a lot of chippiness."
The Lakers took 29 foul shots to 20 for the Celtics in a physical, tightly played game between the longtime rivals.