"We have one second per lap to catch up," he told Germany's Auto Motor und Sport, after Ricciardo finished behind Mercedes' Nico Rosberg on Sunday.
But Horner agreed that Red Bull has finally emerged from the dark and now has a base to build upon for the remaining 18 races of the season.
"Our season began here in Australia," he is quoted by Italy's La Stampa. "We basically skipped winter testing."
That winter season showed that the expected favourite, Mercedes, is currently on track for the 2014 title.
"We knew they would be in front when we got here," Williams' Felipe Massa is quoted by Brazil's Totalrace.
"But the race also showed a strong Red Bull. When they solve their problems with the engine, they will have a car to fight with.
"McLaren showed that they have a good car too, but the race also showed that we have a car to be fighting with them," added Massa, who was punted into retirement by Caterham's Kamui Kobayashi at the first corner.
Winner Rosberg, however, tipped Mercedes to only get stronger from now, revealing the Brackley team will use the two weeks before Malaysia to make the W05 "even faster and more reliable".
Niki Lauda said the German drove "like a god" in Melbourne, while the Welt newspaper said "Rosberg is the new Vettel".
World champion Vettel's Red Bull failed in Melbourne, and the team's Dr Helmut Marko pointed a clear finger of blame at Renault.
"They have underestimated some of the problems (in preparing for the 2014 rules)," he said, "and also not correctly calculated the necessary time frame".
Marko said he hopes the problems are all solved by "the summer", when Red Bull wants "to be close to Mercedes".
Indeed, Mercedes' Lauda said the German squad cannot relax in the face of Red Bull's problems, saying the RB10 is clearly already "really fast".
"That is why we need to develop our car quickly, so that what happened last year does not happen again," he told German television RTL, referring to how Red Bull recovered an early-season dip to utterly dominate in 2013.
Lauda said "thank god" when contemplating that Renault is still grappling with its turbo V6.
Also struggling to face up to Mercedes' current dominance is Ferrari, after Fernando Alonso finished just fifth on the road on Sunday.
"I would have liked to be closer to the podium," the Spaniard is quoted by El Confidencial, "but it was impossible.
"With the Mercedes engines ... it was almost like another category," said Alonso. "I was behind a Force India and it was impossible to overtake.
"Before the race, I could sense that we were behind Mercedes, but maybe not so far," he added.