Aston's Fernando Alonso pitted from second position for medium dry tyres, not the intermediate wet tyre, on Lap 54.
However, the rain intensified suddenly on the next lap. Verstappen came in for intermediates having crawled round on the medium tyre he had started the race on, while Alonso would be forced to come in again for intermediates of his own.
By that time Alonso had lost the chance to get ahead of Verstappen by pitting for the right tyre on Lap 54, something Horner felt was pivotal to the outcome of the race.
"We had enough margin with nine or 10 seconds when he pitted that even being three or four seconds off the pace, we'd have still been three or four [seconds] up the road," Horner said.
"I was surprised they took the medium tyre and that totally got us off the hook and then it was a question of getting it to the pits and having us turn the car around."
He added: "I think in 20:20 hindsight we should have probably pitted one lap earlier to go on to the inters. But thereafter, he [Verstappen] was very mature when the rain came. He took it steady and brought in the tyres and really closed out the race. So really, you know, the top drawer drive by Max today."
Horner pointed out that Verstappen had put himself in that position through his stunning pole lap on Saturday, which saw him edge Alonso by 0.084s by finding a huge chunk of time in the final corners of the lap.
"I think he did 70% of the job in sector three yesterday," explained Horner. "That lap will go down as one of the all-time great laps here in Monaco, I mean, it was stunning."