The Formula 1 star replaced Liam Lawson before the Japanese Grand Prix, but he qualified in 15th behind Lawson after a mistake on his final Q2 run.
Red Bull team principal and CEO Christian, 51, told reporters: "His P1 was very strong, P3 was fine. In Q1, he was only a tenth away from Max.
"In Q2, he made a mistake when he was 15kph quicker than he's ever been into Turn 1. He had a moment and then you're chasing the rest of the lap.
"Qualifying dictated his race, a race where I can't remember seeing any overtakes. Had he qualified higher, he would have finished higher.
"Now he's finding his feet in the team and we will see over the next few races that performance will step forward."
Christian backed Yuki despite the setback.
He added: "He's settled into the team. He's given very good feedback."
In first practice last week, Kuyi finished just one tenth behind teammate Max Verstappen, but he didn't replicate that in qualifying.
Red Bull are focusing on the drivers' title, with Yuki told he should remain close enough to Verstappen to help him strategically.
He told Sky Sports F1: "I am happy with my performance but in terms of the result it's quite tough.
"I wanted to finish in the points. I was expecting more in my home Grand Prix so it is a mixed feeling.
"I am learning and gaining more confidence in the car. I felt controlled towards the end of the race. If I had another qualifying, I'm sure it would have been different.