As the 26-year-old German gears up for his 100th race for Red Bull in Monaco this weekend, Horner told Reuters there was still everything to play for despite Mercedes' current domination.
"It reminds me very much of 2012, which started with us on the back foot and he turned it around and put a run of results together in the second half of the year and then won the championship at the last race," he said.
"Of course, Mercedes are in a formidable position. But nobody has given up on anything and least of all Sebastian. One thing's for sure, he's a true fighter."
In 2012, Vettel - then also the defending world champion - won only one of the first 14 races but strung together a run of four wins in a row to beat Ferrari's Fernando Alonso by three points overall.
Alonso had been 40 points clear of his nearest rival after the 11th round of the season in Hungary but retirements in Belgium and Japan blew the championship wide open.
Mercedes have won the first five races of this season, with Lewis Hamilton taking the overall lead from team mate Nico Rosberg with four victories in a row, while Vettel has made just one podium appearance.
Hamilton has 100 points to Vettel's 45 but there are 14 races left and double points at the final round in Abu Dhabi.
Vettel's relaxed new team mate Daniel Ricciardo, replacing fellow-Australian Mark Webber, has also given the champion something to ponder by outqualifying and beating him in the last three races.
But the German, who has not found the new V6 turbo hybrid powered cars fully to his liking, showed in Spain this month that he was picking up speed when he fought from 15th on the grid to fourth at the finish.
"I just don't think he's had the feedback from the car that he needs," said Horner. "He's very sensitive to corner entry and the car's not been giving him that feeling that he needs.
"I think we've made some advances with the engine management, how the engine is behaving under braking, and with setup and I think we should be getting closer and closer."
Monaco, with its tight and twisty streets rewarding driveability and precision more than outright engine performance, offers a chance to strike back.
"It's very easy to get caught up in the moment and at this moment in time they (Mercedes) are doing a fantastic job and are ahead of everybody else," said Horner, speaking in his team's floating 'energy centre' in the Monaco harbour.
"But as you can see from pre-season to now, which is only two and a half months, we've come a long way. So if in the next two and a half months we can go just as far, hopefully we can really start to challenge them.
"We know we've got a fantastic chassis. The Renault guys are working tremendously hard and are making progress," added the Briton.
Since he joined Red Bull in 2009, after making his debut in 2007 with BMW-Sauber and then moving to Red Bull-owned Toro Rosso later that year, Vettel has won 38 of the 99 races he has started.
The German has stood on the podium 62 times, had 44 pole positions, 23 fastest laps and led 63 races.
"It's a remarkable run that Seb's had with the team," said Horner. "And it's gone amazingly quickly. What we have achieved together is quite phenomenal and the exciting thing is what is still to come."
Vettel won Monaco in 2011 and Horner said that triumph would always rate as one of the driver's many career highlights.
"There's the race he won to win his first world championship in 2010. There's the first win (for Red Bull) in China, there was the win in Monaco when we fitted the wrong tyres," said the principal.
"It was so close, and against the odds, that he did that. There's so many races that he's just been fantastic in that it's difficult to pick out one highlight."
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