"I thought tonight what probably cost us the game was our inability to have consistent success on the offensive end. We had stretches in the second half where we went 6 or 7 minutes without scoring."
Callahan scored 12 points on 4-of-10 3-point shooting and came up with the two big ones.
Davis was 6-of-9 shooting but also committed seven of Tulane's 13 turnovers.
Nick Jacobs scored a season-high 12 points in his first start for the Crimson Tide. Lacey also had 12 points for Alabama, which made just 3 of 15 3-pointers.
Leading scorer Trevor Releford had just six points, 10 below his season average.
Grant did not make any players available for interviews after the game.
"I think I can answer your questions as good as any of them can answer your questions," he said.
Callahan answered with a 3 after Releford's basket put Alabama ahead 45-39 with 4:19 to play to begin his hot finish.
Alabama led by seven points in the opening minutes of the second half before Tulane scored 12 consecutive points for its first lead, 36-31, with 11:54 left. The Green Wave dominated inside with three offensive rebounds before Davis' put-back and followed that physical display with back-to-back 3-pointers by Ricky Tarrant and Ben Cherry.
Tarrant, who had seven points, is from Pleasant Grove, Ala., about 50 miles away. He struggled to 2-of-12 shooting for five points but also got four assists and a win over his home state team.
"Ricky's an emotional guy to begin with," Conroy said. "He's probably still jumping up and down in that locker room, I would think."
Alabama made one basket in the opening 9 minutes of the second half before Jacobs got hot. He scored six points during Alabama's 11-0 answering spurt sparked by full-court pressure that forced a couple of turnovers and fast-break baskets for a 42-36 lead with 7:14 to play.