Red Bull currently run Tag Heuer-badged Renault engines and they had been expected to challenge Mercedes in 2017.
Horner's team are third in the Constructors' Championship and are now 237 points behind the Silver Arrows after Lewis Hamilton won the Japanese Grand Prix.
Both Daniel Ricciardo and Max Verstappen have struggled to claim a pole position this season and Horner believes his team will struggle unless they can adapt their power unit.
He told Sky Sports F1: "We run in the same modes in the race as we do in qualy. It's a big difference.
"We gave away [on Saturday] the best part of a second but in the race, the chassis has been strong all weekend. We can see from the GPS overlays that the chassis is right there but obviously [Mercedes] can't run in those high power modes for the duration of the race.
"The qualy modes are vital [to a championship challenge] because you can't leave all the work to be done on a Sunday."