The Italian junior outfit had been using the same Renault engines as its parent team since the start of the latest turbo era in 2014, but announced at the end of last year that it would return to the Maranello fold .
Although Toro Rosso will run year-old power units, Horner says Ferrari’s late-2015 engine specification still represents a massive step forward.
“Toro Rosso has bolted in 0.8 seconds into their car through a different power unit,” the Red Bull team principal told reporters at the new livery launch in London.
“That is a significant amount of performance. We are hoping to make similar gains throughout the year but obviously the chassis is going to have to prop that up.”
Since securing four consecutive championship doubles from 2010-13, Red Bull has slipped down the pecking order and is coming off its first winless campaign since 2008.
While Horner does not expect to challenge the likes of Mercedes and Ferrari right off the bat, he is confident his team has what it takes to make noticeable strides in its recovery to the front.
“It is going to be a season of evolution for us. I think it is probably going to be a season of two halves; the first half is going to be less competitive than the second but we are expecting to make significant progress during the year.
“I think most teams have probably written Red Bull off for this year. We are fighters and focused on getting ourselves into a competitive position and I think it would be foolhardy to write a team off with the calibre of people Red Bull has.”