The Milton Keynes-based marque failed to score any points in a race for the first time in almost two years in Sunday's Italian Grand Prix.
Reigning champion Sebastian Vettel incurred an alternator failure for the second time this year when running sixth at Monza, the other when he was leading the European GP in Valencia in June.
That left Horner throwing his head in his hands before Mark Webber retired a lap from home after flat-spotting his tyres in a spin shortly before.
The upshot is Vettel and Webber have fallen 39 and 47 points adrift of title leader Fernando Alonso, whilst Red Bull's advantage in the constructors' championship over McLaren has been whittled down to 19 points.
Assessing the prospects of holding on to both championships for a third consecutive year, Horner said: "The most important thing is we need to rectify the faults that have occurred.
"DNFs (did not finish) are extremely expensive and it is our first no points scoring race since 2010 - which also happened to be an engine failure that cost us on that day as well.
"We cannot afford to not be finishing races. It makes the mountain higher, but both the drivers are still in the championship race, and we still lead the constructors' by 19 points.
"With seven races to go we have to make sure we throw everything at it.
"There is a lot of racing still to do, and we are a strong team."
Particularly crippling for Red Bull at present, aside from the two failures on Vettel's car, has been their lack of pace at the last two races which have been power tracks.
With Singapore's Marina Bay street circuit up next in a fortnight, its tight, twisty nature should suit the team's car more, but Horner knows he can take nothing for granted.
"Sebastian, with the lap he did in qualifying on Saturday, it was absolutely everything there was," said Horner.
"You only have to look at an audio overlay to see where we haemorrhaged the time.
"In the race Seb was really hanging on and doing a really strong job.
"He managed to hold on to Jenson (Button) early on in the race, but then the Ferrraris were just too quick on the straights for us.
"We were just powerless to defend, but Sebastian did nothing wrong. He drove as hard as he could.
"Monza unfortunately exposed our weakness.
"We should hopefully be more competitive in Singapore, but as we have seen in 2012 there are no guarantees."