“If we are going to make a championship of it, we’ve got to take the fight to them,” Horner, whose team have just one podium finish so far this year, told Sky Sports television.
“We’re going to give it everything. I believe we can take the fight to them, we just can’t concede too much more ground.”
“We were 22km an hour slower on that kilometre straight today, that represented almost 100 metres that we’re giving away on the straight. That’s where we’ve got to improve.
“We know where we’ve got to fix our issues and hopefully there’s some steps towards that in Barcelona,” added the Briton.
The next race is the Spanish Grand Prix on May 11, with all the teams sure to bring upgrades after the three-week break.
Red Bull’s design wizard Adrian Newey skipped Shanghai to work on improvements and his rivals need no reminding about his reputation.
“The Red Bulls are famous for coming back and Newey is there,” Niki Lauda, non-executive chairman of the Mercedes team, warned on Sunday evening. “He wasn’t here so he sends something new for Barcelona, I’m afraid.”
Australian Daniel Ricciardo finished fourth for Red Bull in China, with quadruple champion Vettel fifth after being ordered to move aside for his younger team mate for the second race in a row. The German did so, but only after initial reluctance.
Horner had only praise for Ricciardo, who has had the better of Vettel in three races.
“He’s just Joe Cool, isn’t he? He’s always smiling,” Horner said of the Australian. “And he’s quick. we knew he was quick but he’s exceeded all our expectations so far.
“He’s so cool under pressure. I don’t know whether you hear any of his radio but it’s like he’s having a chat at a coffee bar,” he added. “You wouldn’t think he’s in a grand prix.
“He’s been enormously impressive since the start of the season in Melbourne. His confidence is growing, you can see that.”
Ricciardo has outqualified Vettel three times but Horner said the German would fight back.
“We know that Seb is very sensitive to the car, how it enters into a corner and at the moment he hasn’t got the feel that he needs from the car,” he said.
“As soon as he gets on top of that, bang. He’ll be right back,” added the team boss.
Vettel, winner of nine races in a row at the end of last year, has made slow starts before and still come out on top but he faces his biggest challenge yet.
The new Mercedes power unit has been the pick of the grid while Red Bull’s partners Renault are still playing catch up.
Although Red Bull have now clawed their way back to second in the constructors’ standings, they are 97 points behind Mercedes. Vettel is fifth in the drivers’ championship, 46 adrift of Mercedes’ Nico Rosberg.
“He’s a deep thinker and he’ll analyse this,” Horner said of the Chinese race. “One thing he does incredibly well is look inwardly at where he can improve, where can he be better, what is the other guy doing that’s giving him that advantage?
“Sebastian is an absolute fighter and we’ve seen that before… we’ll sit down and talk it through but he won’t need motivating, that’s for sure.”
(Reporting by Alan Baldwin, editing by Pritha Sarkar)