Gasly recorded his first points finish for the team at the weekend - securing a P8 finish - but not even being able to reach Q3 for Red Bull.
The Frenchman's start to life at Red Bull has been far from ideal, with Gasly being eliminated from qualifying in Australia a couple of weeks before the Bahrain GP, and only managing 11th-place on his debut for the side.
Max Verstappen, his team-mate, secured a first ever podium finish in Melbourne and then finished in fourth-place in Bahrain.
However, Horner does not want to be too downbeat about Gasly's start to life at Red Bull and believes he should take some confidence from his performance at the weekend.
"I think it was important for Pierre to have a strong race (in Bahrain), and he did that," the Red Bull team principal said. "I thought some of his overtakes, particularly on (Sergio) Perez, which I don't think went on the main-screen, was very impressive.
"His pace in clear air, particularly in the second half of the race, was strong so I think he would've taken a lot of confidence out of that. I think once he starts qualifying further up the grid then life will get a lot easier for him.
"I think it will have been a good boost of confidence for him. He's raced competitively, raced hard, he's had to overtake quite a few cars and you know, being competitive particularly in the second half of the race. I think he can take a lot out of this weekend and you know carry that into future races."