Rasheed Wallace had two points and two rebounds in 13 minutes in Game 1.
"[Wallace] has to play better, bottom line," said Rivers, who has given Wallace plenty of rope this season. "He has to play better defense -- the offense will come -- but he has to be a better defender. And we can't wait for him. He has to be a better defender for us."
Wallace, underwhelming for much of the 2009-10 season, continues to provide little in the way of production in the postseason despite all the playoff experience he brought with him to Boston. After logging a mere two points and two rebounds over 13 minutes in Saturday's Game 1 loss, Wallace is now at minus-20 in the plus/minus for the postseason, the lowest number on a team that's won four of the six games it has played.
Rivers on Sunday seemed unwilling to completely yank Wallace from the rotation, but noted that Williams won't be overlooked.
"[Williams] enters the discussion every day," Rivers said. "He's definitely in the discussion, there's no doubt about that."
The 35-year-old Wallace is averaging 3.5 points on a mere 35 percent shooting and two rebounds per game this postseason. This from a player who has averaged 14.2 points on 44.5 percent shooting and 6.5 rebounds over 159 career playoff games. What's more, he's slow to react on defense, often getting raced past by ball-handlers and struggling to corral 50/50 balls against more athletic big men.
Simmons: Smoke and mirros with Wallace
Earlier this season, a frustrated Sports Guy penned a column on why he can't stand Rasheed Wallace. Bill Simmons
Asked if Wallace's minutes could be on the decline, after already slipping in the first round, Rivers said simply: "It could be. The bottom line is he has to play better. And we'll give him every opportunity to play well."
Williams, who is playing in his first playoff series in his four years in the league, has appeared in only one game, logging 18 minutes against Miami in Game 2 of their first-round series. Kevin Garnett was suspended for the game.
Asked before that game about more potential playing time, Williams said he didn't change his preparation.
"You prepare like you prepare for every game," he said. "If it happens or if it doesn't happen, you go in the same way... Like I said, I go into the game preparing to play, and if it plays out like that, I'll be ready."
Wallace is clearly the superior player when he plays to his abilities, but his abilities appear to have diminished rapidly this season. Even making a number of starts for an injured Garnett, Wallace did not register a single double-double this year. Even Williams registered one double-double at the start of the year while playing in place of injured Glen Davis.
Chris Forsberg covers the Celtics for ESPNBoston.com. Follow him on Twitter.