Early leader Verstappen was brought into the pits on lap 10 of the Azerbaijan Grand Prix after starting to struggle with his rear tyres and being put under pressure by team-mate Sergio Perez.
Moments before the decision AlphaTauri's Nyck de Vries had stopped on track after clipping the wall in Turn 5 and as the safety car was brought out, the move backfired on Red Bull.
With Verstappen having dropped to third, Perez and Ferrari man Charles Leclerc managed to make cheap pitstops and stay ahead of the Dutchman.
While the world champion made short work of passing Leclerc at the following restart, the timing of the pitstop meant Perez was handed a clear run to victory, which he duly brought home with a measured performance.
Questions were raised on why Red Bull would decide to pit Verstappen knowing there was a stationary car on track, especially on a narrow street circuit of Baku where safety cars interventions are numerous.
"At the time we decided to pit Max because he was starting to struggle a little bit with the rears of his car and Checo was obviously right up behind him," said Horner.
"So, we decided from a strategy point of view it was the optimum time to take the stop."
In the short snapshot available of De Vries' stationary car, Red Bull hadn't spotted that the AlphaTauri suffered terminal damage because the Dutchman had clipped the inside Turn 5 wall and bent his front-left corner.
"From the glimpse that we got, all four wheels were on the car, he hadn't hit the barrier and the engine was running," Horner added.
"It looked like he'd select reverse and carry on, so you'd never expected that to go to a safety car.
"Usually, if you see a car in the barriers here it's a safety car, but there was no sign of it.
"It was only subsequently on the replays that you were able to see his track rod was broken."
Red Bull even considered bringing in Perez as well for a double stop to avoid being undercut by Leclerc.
"Obviously, with 20/20 vision you would have just done one more lap and go from there," he added. "But you just don't know at that point whether Charles is going to pit and then he suddenly he jumps both of them.
"We were a one stage were talking about gearing up for a double stop. It was one of those things that sometimes you get lucky and sometimes you don't."
After an uneventful final stint on hard tyres Perez and championship leader Verstappen secured Red Bull's third 1-2 of the season, with Perez closing the gap to Verstappen to six points.
