By Brian Lewis in Boston and Zach Braziller in New York

Jeff Green’s injury presented Nic Claxton with a golden opportunity to seize more minutes and solidify an even bigger role in the Nets’ playoff rotation.

That didn’t happen Friday.

Claxton was wildly inconsistent in the Nets’ 125-119 loss at Boston in Game 3 of their first-round series, getting roughed up physically by Tristan Thompson and an angry Celtics team.

Thompson had 19 points and 13 rebounds, including a staggering nine offensive boards — one fewer than the Nets had as a team.

“I don’t know that Jeff, his strength is gonna be keeping Thompson off the glass. But we certainly miss his versatility, his ability to play multiple positions and multiple roles,” coach Steve Nash said. “Nic had an up-and-down night. Young player trying to figure it out in a big moment.

“That’s going to come for Nic. We believe in him, we want to support him. Anyone can play for us; you look down our bench, we believe and trust in all these guys. There’s probably not enough minutes to go around, but we can always push different buttons and play different guys and that kind of happens from a judging the flow of the game standpoint.”

Claxton had four points and five rebounds, but committed a pair of turnovers, shot just 2-for-5 though all of the attempts came in close, and finished a minus-21.

The only Net with a worse plus-minus was Landry Shamet, who was a ghastly minus-26.

In a game in which it was expected the Celtics would come out hungry and physical, the Nets failed to match that edge. Bruce Brown played just 14:33, with Nash doubling down on shooting and offense by going to Tyler Johnson before Brown.

Any potential Nets second-round series against Milwaukee would start June 5, a week from Saturday, if the Nets and Bucks close out their series in five games. The second-round series would begin June 7 if either series gets extended to six or seven games.

The Bucks will be without starting off-guard Donte DiVincenzo for the rest of the playoffs. He has a torn ligament in his left ankle.

DiVincenzo, 24, averaged career-highs of 10.4 points and 5.8 boards in 66 starts.

“It’s a tough blow,” Bucks coach Mike Budenholzer told reporters. “But you have to kind of process and understand it’s an unfortunate thing, but we have to prepare and get ready.”

Green (left plantar fascia strain) won’t be reevaluated until at least Sunday June 6, according to Nash.

“We’ve had that the next-guy-up mentality where guys have to fill in. And it may take a game or two to figure that out,” Kyrie Irving said. “But this is the playoffs. We’ve just got to figure it out on the fly.”

James Harden’s seven 3-pointers tied a Nets playoff record, set by Joe Harris in Game 2 and Deron Williams in Game 4 of a 2015 first-round series against Atlanta. Harden had just the third 40-point game in team playoff history.

Harden and Kevin Durant (39 points) are the second set of teammates in Nets playoff history to top 30 points in the same game.