Lawson started the race at Circuit of the Americas from 19th and charged his way through the field on a one-stop strategy to score two points.
It marked the first time since the Belgian Grand Prix that RB had scored drivers’ championship points.
“It’s a sample of one and I thought he looked like a veteran, to be honest,” Horner told Sky Sports F1.
“He’s a great racer. I think he can be very happy with that drive today.
“He drove a great grand prix. Starting 19th, finishing in the points, some great overtakes, so he should be pleased with that.”
Lawson’s appointment at RB in place of Australian Daniel Ricciardo comes with plenty of speculation.
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The Kiwi didn’t shy away from chatter about his future inside the Red Bull fold, whether that be staying with RB into 2025 or potentially replacing Sergio Perez at the top team.
“The goal every weekend is points. I know that they have an expectation on me but at the end of the day I’ve got an expectation on myself as well to do a job,” said Lawson.
“I want to stay in Formula 1 and have a full-time seat next year and these races are my key to doing that.
“From my side, I’m taking it weekend by weekend. This weekend we were strong. We need to now focus on Mexico.
“I’m well aware of obviously the expectation they have on me but at the end of the day it’s been like that since I was 16 years old as a junior.
“They’ve always put that pressure on us so realistically it’s no different to that.”
Lawson said he spoke to Red Bull Racing team principal Christian Horner and advisor Helmut Marko, who were both pleased with his performance.
“I spoke to both Christian and Helmut and they were both positive,” said Lawson.
“They were happy. They said well done, but I guess at the same time that was the expectation they had on me.”
Lawson will have very little time to celebrate his two points with a one-week turnaround for the Mexico City Grand Prix on October 26-28.
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