"I thought it was kind of a flat game in the beginning," Sixers coach Maurice Cheeks said.
Philadelphia was 2-of-11 from 3-point range. Over the last three games, the Sixers have hit just 5-of-37 3-pointers, including an 0-for-14 effort in last Friday's one-point win over Washington.
"We've got to find a way to put the ball in the hoop," Korver said. "We're just not able to get good shots."
The Hawks led 66-62 after the third quarter and extended their lead to nine on several occasions.
Atlanta led 79-72 before Childress hit a 3-pointer from the baseline and Johnson converted a three-point play for an 85-72 lead with 1:41 remaining.
Woodson pointed to his team's defense during the key 6-0 run.
"We've been playing good defense in the fourth quarters," he said. "Tonight we made a stance in the third quarter and it carried over into the fourth."
Green was 7-for-7 from the field in the second quarter and scored 16 points, as the Sixers overcame a seven-point deficit to take a 46-45 halftime lead.
Smith's 3-pointer at the buzzer had given the Hawks a 24-17 lead after the first quarter.
Woodson was an assistant coach with the 76ers from 2001-03. ... Hawks C Zaza Pachulia took an inadvertent forearm from Philadelphia's Samuel Dalembert and fell hard to the floor with 6:28 left in the first quarter. Pachulia left the game with what a team spokesman called "headaches" and did not return. Pachulia played a total of 28 seconds. ... The Sixers have lost six of their first nine home games. "We have to establish some consistency at home," Cheeks said before the Atlanta game.