Verstappen won his eighth consecutive race before the summer break at Spa to extend Red Bull's clean sweep of winning all of 2023's 12 races so far, which is an all-time record.
Red Bull has now bagged the past 13 grands prix, a record that would have extended to 23 if it hadn't lost out to George Russell and Mercedes in last year's Brazilian Grand Prix.
But despite the team's unprecedented dominance with its all-conquering RB19, team principal Horner refuted any concerns over complacency setting it at the Milton Keynes squad.
"I don't think so. I think we're very much taking it one race at a time, one session at a time," Horner said. "And I think you have to focus like that.
"Nobody's allowing their mind to drift and I think that it's a long, long championship."
There's a lot going on behind the scenes with Red Bull Powertrains, as that's gearing up as well in the background in Milton Keynes, with 2026 not being all that far away now. So, plenty to keep people focused on."
Red Bull has received "numerous approaches" from rival teams to poach its best staff, with Rob Marshall one key figure heading to McLaren, although it has equally headhunted hordes of engineers to set up its new engine division.
Horner thinks that with the target on Red Bull's back only getting bigger, the challenge of staying at the front grows correspondingly. But he feels Red Bull's "strength in depth" leaves it well-equipped to arrest any decline.
"The challenges are always different because, when you're the hunter, you've got everybody focussed on the target ahead of you," he explained.
"When you suddenly become the hunted, it's a different type of pressure.
"Of course, we have numerous approaches from all these guys, chasing all our staff, sponsors, you name it.
"Getting there is one thing, staying there is another. But I think the spirit, the culture that we have within the team; we've got great strength in depth and have enjoyed great continuity over a long period of time, which again is so important in this business."
