Red Bull lodged two protests after Mercedes driver George Russell took victory in Montreal, citing concerns over the British driver leaving too much of a gap behind the safety car and driving erratically during the closing stages of the race, which finished under safety car conditions.
Despite the stewards ultimately rejecting the protests, Horner said the team had every right to raise the issue and had no regrets about doing so.
“It’s a team’s right to do so,” Horner told Sky Sports F1 at the premiere of F1: The Movie.
“We saw something that we didn’t think was quite right, and you have the ability to put it in front of the stewards, and so that’s what we chose to do.
“[We have] absolutely no regrets in that.”
Max Verstappen finished second behind Russell in the race and, with Lando Norris’s late retirement, moved to within 21 points of the McLaren driver in second place in the Drivers’ Championship.
Horner said there is still plenty of opportunity for Verstappen to gain further ground in the standings and push towards a potential fifth consecutive championship.
“We’re not even halfway distance yet,” he added. “We had a good weekend in Barcelona. We won in Imola a few races ago, and as Sunday proved, anything can happen.
“You’ve just got to hang in there. And it’s a long championship. We don’t give up on anything. You keep fighting until the very end.
“If one person is going to do that, it’s definitely going to be Max.”
Red Bull heads to its home race in Austria next weekend, having won four of the last seven races at the Red Bull Ring.
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