Popovich missed the game while dealing with "personal business," according to the team. He is expected to return to the bench for Friday's game against the Brooklyn Nets.
The team would not say if Popovich made the trip to Charlotte.
"It's night and day to be in the big-boy chair," Duncan said. "But truth be told, I wasn't in the big-boy chair. We've got [Spurs assistants] Becky [Hammon] and Will [Hardy] and Mitch [Johnson]. Mitch prepped the game for us, Becky and Will were making all the calls, and I was the only one just standing there screaming at people -- nonsensical stuff.
"So we did it coach by committee, and it could've been any one of us up there and we would've done exactly the same stuff."
Asked if being a head coach is something he wants to pursue down the road, Duncan said, "Nope. Pop is going to be back, and I will be happy to hand it right over to him."
Duncan: Happy head-coaching debut is over
Tim Duncan says it is a "night and day" difference between being an assistant coach and head coach after the Spurs win vs. the Hornets.
Duncan said that when his team had a five-point lead late in the game, he thought the Spurs might cruise to a win.
"But they had to make it interesting. I think they did that out of spite," he joked.
Hornets coach James Borrego, who worked as an assistant coach for the Spurs when Duncan was a player, said it was "odd" to look down at the other bench and see the 15-time All-Star coaching a team.
"I'm used to seeing that No. 21 on his jersey and see him out there leading the group. Tonight he had a blazer on," Borrego said.
Borrego said he has immense respect for Duncan.
"I wouldn't be sitting here [as a head coach] if it wasn't for that guy," Borrego said.
Duncan was mostly mild-mannered on the bench, not showing much emotion as the game progressed. However, he challenged a charge call on Derrick White with 9:09 left in the fourth quarter, but the play was not overturned.
"He obviously has that presence that everyone likes to listen to what he says, and you know he's very calm in situations and very constructive, and everyone listens and goes out and tries to accomplish that," Patty Mills said. "So it was good to see everyone dialed in to what he was saying."
The Hornets jumped to a 12-2 lead to open the game, prompting Duncan to use his first timeout. Charlotte extended its lead to as many 17 in the first half, but the Spurs battled back to take a 77-76 lead entering the fourth quarter.
San Antonio extended the lead to six with 4:24 left in the game after three free throws by Bryn Forbes, just moments after he appeared to get away with a travel in the lane that drew boos from the Charlotte crowd.
The Hornets came back, and Terry Rozier cut the Spurs' lead to one with a driving layup with 42 seconds left. After DeMar DeRozan missed a pull-up jumper, the Hornets had a chance to win on their final possession. However, after Rozier drove to the basket, his pass under the basket went in and out of the hands of Cody Martin, allowing the Spurs to escape with just their fourth win in the past 12 games.
"It was fun just getting in the huddles, especially for a guy like me who had the privilege to play against Tim," DeRozan said. "Now to be sitting in the huddle, listening to him coach, it was great."
Earlier this season, Duncan was the acting head coach when Popovich was ejected during a loss to the Portland Trail Blazers on Nov. 16. Tuesday's Spurs win still counts toward Popovich's coaching record.
Duncan spent his entire 19-year career with the Spurs and has been an assistant coach since July.
The 43-year-old won five NBA championships with the Spurs and is a finalist for the Naismith Memorial Basketball Hall of Fame later this year.
The Associated Press contributed to this report.