Max Verstappen headed Sergio Perez to the flag on Sunday, Fernando Alonso third more than 30 seconds adrift of the race winner.
Ferrari struck reliability trouble with Charles Leclerc while tyre issues hampered Carlos Sainz in the other car and limited him to no better than fourth.
Mercedes meanwhile has conceded its car isn't good enough this year, with Toto Wolff suggesting his team has lost ground rather than made it up over the winter.
Despite a dearth of apparent rivals, Horner is mindful that only a single race has been run at this point.
“We've only got one data set,” he noted.
“We're not taking anything for granted.
“Let's see Jeddah in two weeks, Melbourne after that.
“I think once we've got two or three circuits under our belt we'll get a much better picture of strengths and weaknesses of our car and our opposition.
“But certainly a very healthy start and a very well-executed race to bring in those points.”
Such was the performance advantage of Red Bull in Bahrain that some have, only half tongue in cheek, questioned whether Verstappen could win all 23 races this season.
“23 races is a marathon and it's about being consistent over the campaign,” Horner said when asked about the potential for a perfect season.
“[Bahrain] was a great start, both drivers; obviously Checo [Sergio Perez] lost out at the start, the dirty side [of the track], the benefit of the brand new tyres off the start line for Charles [Leclerc].
“But again, the strategy and the pace we had enabled Checo to pass him and then it was a question of managing the race to the finish.
“We fully expect our rivals to come back hard in the future races.”
Round 2 of the F1 season is next weekend's Saudi Arabian Grand Prix, an event which last year saw Verstappen outfox Leclerc to take victory.