Gasly has been out-performed by his team-mate Max Verstappen during his first three races as a Red Bull driver - with the former Toro Rosso man managing his best finish for his new team with a P6 in China.
"I think he's made a step forward this weekend," Horner said on Gasly following the race in Shanghai. "But I think he is still not totally comfortable within the car at the moment.
"Not (in terms of) physically fitting, but he is in the process of needing to refine his style to optimise the best from the car, the car's characteristics, and he is making progress with that.
"I think it is proving to be a challenge for him but he is making progress and I think getting the tastest lap at the end of the race gives him confidence."
The French driver is still getting to terms with his new car, but a sixth-place finish in Shanghai is certainly something to build on, when the Formula 1 calendar comes round to Baku in Azerbaijan next weekend.
Being behind the talent of Verstappen is certainly not something to worry about too much - he just needs to keep plugging away below him and earning valuable points for Red Bull.