Allen, Kevin Garnett, and Paul Pierce all had opportunities to put the Celtics ahead in the final minutes, but Rivers said the team could have made a better effort to get Allen open.

“Ray, we’ve got to get him better shots,’’ Rivers said. “We’ve got to get Ray shots. Paul’s got to be more aggressive. But that’s on us with Ray — on our team, on our bigs. Ray should have gotten better shots and we didn’t get him open. There were ample times to get him open and we didn’t do a good job. Ray’s going to get open.’’

Allen finished 6 of 14 from the floor, 2 of 7 from 3-point range. He took just two shots in the fourth quarter — a missed three with about four minutes left and another nearly a minute later. He shot below 50 percent for the first time since going 2 for 9 in Game 1 of the Celtics’ first-round series against the Heat.

Allen averaged 19.4 points against Miami. The Celtics registered their biggest win of that series, a 106-77 Game 2 blowout, when Allen caught fire from deep, drilling 7 of his 9 shots from long distance.

Point guard Rajon Rondo said it’s no coincidence that when Allen’s shot is falling the Celtics’ offense is cruising.

“[The game] changes,’’ Rondo said. “It changed in Miami. Ray drew so much attention . . . It hurt the defense, because what adjustments are you going to make? You come out to Ray and you trap him, he’s making the next pass and Kevin’s scoring or [Kendrick Perkins] is scoring. If you don’t, he’s still going to knock down the shot. So it’s pick your poison with how you’re going to defend him.

“When he’s making shots we’re really difficult to defend.’’

Shaquille O’Neal went 4 of 12 from the floor, 3 of 4 from the stripe. He scored three of his four baskets in the fourth quarter, including a tip-in with 1:02 left that put the Cavaliers ahead, 98-93. His field goals were a dunk, a layup, a 4-foot hook shot, and that tip, and those are baskets Rivers said the Cavaliers’ hired giant shouldn’t get without being bothered in the process.

“I think we should hack Shaq when he has a layup,’’ Rivers said. “But I think that was in the game plan four years ago. So that hasn’t changed. I don’t know about the whole Hack-A-Shaq thing. Honestly, LeBron James, Mo Williams, all of them, they got layups and they all stood. We got layups and we were on the floor, peeling each other up [off it].’’

Davis picked up three fouls in five minutes in the first quarter. He was on the floor for all of 38 seconds in the second quarter, making a quick layup, then picking up his fourth foul. He played six minutes in the second half, hacking James early in the fourth quarter for his fifth foul. At that point, he was officially hamstrung.

“I got too many fouls too early so I couldn’t help my team,’’ Davis said. “I’m kind of like an aggressive fouler, and I couldn’t really do that. It changes the game.’’

Julian Benbow can be reached at jbenbow@globe.com.