The Celtics shot 33.3 percent from the field, somehow staying in contention until the final minutes, in setting up Game 7 of the Eastern Conference semifinals at TD Garden on Saturday.

“We didn’t have it,’’ Rivers said. “They played with a lot of energy and a lot of energy from the building. I thought they outplayed us.’’

At least the Celtics were consistent, putting together four quarters of poor shooting, never shaking out of their slump. The Celtics went 6 for 19 in the first and third quarters, 7 for 22 in the second quarter, and 7 for 18 in the fourth quarter.

The Celtics failed to get their running game going and struggled in the half-court game. Even when the Celtics had wide-open looks, they misfired. As a team, the Celtics had 14 assists. Rajon Rondo, averaging 13.2 playoff assists before this game, had one of his least productive games, with six assists and four turnovers.

The Sixers did not fare much better offensively. And the Celtics still had hope of pulling this one out in the fourth quarter.

A Ray Allen 3-pointer out of a timeout cut the Celtics’ deficit to 78-72 with 1:41 remaining. The Celtic defense kicked in, but Sixers center Lavoy Allen tipped a rebound off Rondo, extending what became a 47-second possession, the Celtics getting a timeout with 48.8 left.

Ray Allen had a chance to pull the Celtics within 3, but missed a 3-point try. And Andre Iguodala, who missed his first four free throws shots of the game, clinched the win with two with 38.7 left. Paul Pierce converted a 3-pointer 5.8 seconds later, then Ray Allen fouled out and Jrue Holiday converted two foul shots. Pierce and Keyon Dooling missed last-chance 3-point attempts for the Celtics.

“I thought we had a lot of empty possessions,’’ Rivers said. “We never established Kevin Garnett. Even though Kevin had points, it wasn’t the points we needed, the type of points.’’

The result might have been much worse for the Celtics, but for 20-of-23 free throw shooting and the play of Pierce (24 points, 10 rebounds) and Garnett (20 points, 11 rebounds).

The Celtics shot 26 for 78 from the field, and seemed powerless to capitalize when they found themselves open. Of their first 17 field goals, five were on follow shots, by Ray Allen, Brandon Bass, Mickael Pietrus, and Rondo, who had two. Off-target was an understatement for nearly every Celtic.

Ray Allen, struggling to recover from an ankle injury, was 4 for 11, his performance affected by added defensive responsibilities in the absence of Avery Bradley (shoulder). Bass, who carried the Celtics with a 27-point performance in Game 5, went 2 for 12, with no field goals after the 3:03 mark of the opening quarter.

“They did a couple of things,’’ Rivers said of the Sixers’ defense. “They didn’t trap as much. They waited for our guys to put the ball on the floor and then they went. I thought our spacing was horrendous, so even if they didn’t trap, they didn’t have to, because we were standing next to each other a lot. They allowed Ray to get loose and he just didn’t make shots.

“But I think that will be good for Ray going into the next game because I think he knows he’s going to get shots now.’’

The Celtics actually set the tone early as Pierce aggressively went to the hoop, his play paying off as Iguodala got in foul trouble. The Celtics used a 17-11 second quarter to take a 3-point halftime lead.

But the Celtics went the opening 5:27 of the second half without a field goal, falling behind, 46-41, before Rondo’s follow and Pierce’s 3-point play tied the score with 6:12 left in the third.

Garnett finally started finding the range, converting six jumpers in the final 13:48 of play.

But the Sixers upped the advantage to 11 points early in the final quarter.

Holiday drove following an Elton Brand offensive rebound, Evan Turner made a free throw after drawing a Garnett foul with 1.1 on the shot clock, and Lou Williams hit a pullup to make it 70-59 with 7:15 remaining.

Two Pierce free throws and a Garnett jumper cut the Celtics’ deficit to 7 points, the Sixers calling a timeout with 6:06 remaining.

In the final four-plus minutes, the Celtics went to a three-guard lineup, Marquis Daniels making his first appearance of the game. But Williams made it 72-63 out a timeout and Turner maintained the 9-point lead after a Garnett jumper, the Celtics calling a timeout after Pierce was trapped near the scorer’s table with 3:49 remaining. Rondo missed an 18-footer out of the timeout and Holiday scored in transition for 76-65 advantage with 3:15 left.

Frank Dell’Apa can be reached at f_dellapa@globe.com.