The Milton Keynes outfit has got its 2023 season off to a dominant start by logging 1-2 finishes in the first two rounds of the season.
However, Horner expects other teams to make progress, and stresses that Red Bull has to make the most of its early advantage.
"It's so early in the season,” he said in an interview on a Sky TV business programme. “I mean, it's a 23-race calendar, we've done two races in Bahrain and Jeddah so far.
“And the venues vary a great deal, it's Australia in just over a week's time, so I'm sure it's going to ebb and flow. But we're hopeful that we can extract more performance from the car.
“The regulations are still relatively young. It's only the second year of these new regulations. So I'm expecting to see an awful lot of convergence during the course of the year, and the grid is going to tighten up.
“So we need to make hay while the sun shines at the moment while we've got a competitive car, and just keep pushing through the season.”
Horner stressed in Jeddah last weekend that it was vital that the team got off to a good start with the RB19 given the obvious restrictions imposed by the cost cap penalty.
That would have made it hard to do the sort of fire-fighting that other teams are now having to pursue as they try to close the cap, and in some cases by expensive changes in concept.
“It was so critical for us to come out of the blocks competitively," he said when asked by Autosport if he was surprised that other teams had tripped up.
"The wind tunnel reduction has applied since last October. So we couldn't afford to miss the target with that limited running, because you'd never be able to engineer your way out of that with that handicap.
“So the team have done an amazing job and the RB19 has been the best start to a season we've ever had.
“We're only two races in, but to have had two 1-2 finishes, and be one point off the maximum score, I don't think we could have ever dreamed about that coming into the season.”
Asked how satisfying the strong start was he said: “I think the team is operating at an incredibly high level, throughout the organisation, because you don't get a result like this by just one department doing its bit.
“It's all aspects. Whether it's the aero team, whether it's the design office, whether it's vehicle dynamics, whether it's the production side, the business operationally.
"What you see trackside is such a small percentage of who we are, and this is testimony to that work that goes on behind the scenes.”
Additional reporting by Jonathan Noble
