With three laps remaining on Sunday, Verstappen was promoted to second place after Valtteri Bottas sustained a puncture. Red Bull pitted the Dutchman as it had all but secured second, and was attempting to go for the fastest lap.
However, on the final lap, race leader Lewis Hamilton also had a puncture and limped over the line with three wheels to take his third successive race win.
Horner brushed off suggestions that Max was sure to win the race without his late stop, stating his hard tyres, which were fitted on lap 13, were not in great shape.
“Right at the end there, Max was really getting worried about the vibrations,” Horner told Sky F1. “We saw Bottas had his puncture, we could see we got a big groove on our tyre.
“So we elected to pit and put the soft on, try and bag the point for the [fastest] lap as well. The tyre that has come off Max's car has got a deep groove and quite a lot of lacerations in it as well.
“There's no guarantee that he would have got to the end of the race and then it would have been a completely different story again.
“Lewis rode his lap, they had a great car today and he managed to get it home. Second place is still a really good result for us.”
Aside from the late puncture drama, Mercedes was unchallenged throughout the race on Sunday, as both Hamilton and Bottas stretched out ahead of Verstappen in the opening phase of the race.
Horner believes the world championship leaders were doing a lot more tyre saving during the race, which saw the gap stabilise.
“I think they managed to get themselves sufficiently up the road and then they were controlling the pace. We could see, because the front tyre was a concern here, they were taking it easy in Turn 1, Turn 2, Turn 9 more so than we were.
“So we were surprised to see them get into the issue that they had. We were already thinking about a stop ten laps towards the end.
“It was a surprise to see those issues come up in the last couple of laps, whether there was debris out there that caused the issue, but it was frustrating.”
F1 remains in Silverstone, with the 70th Anniversary Grand Prix taking place next weekend - however a big question mark remains over the tyres, as Pirelli is set to bring tyres that are a step softer than last weekend's, while the weather is expected to be much hotter.
“I would think most people are going to do a two-stop next week,” Horner commented. “It's supposed to be hotter, if you can believe the forecast, we're supposed to be back into higher temperatures.
“We know the Mercedes is a bit more uncomfortable in those temperatures. We've got some performance to find, we're working hard. We've made a step here from Hungary, we've got to keep our head down and keep trying to get stuff to the car.”
Bahrain International Circuit - Winter testing