Prior to Sunday's Japanese Grand Prix at Suzuka, McLaren had been the car to beat for four races in a row, but they were given a rude awakening as Red Bull dominated qualifying and the race.
Lewis Hamilton and Jenson Button could only finish fifth and fourth respectively and their title hopes are fading fast.
Mercedes-bound Hamilton is 42 points adrift of championship leader Fernando Alonso, and 38 behind Suzuka winner and new title favourite Sebastian Vettel, with five races remaining.
Button, meanwhile, is 63 points adrift of Alonso.
A repeat of the demonstration run Vettel enjoyed in Japan at this weekend's round in Yeongam would leave McLaren's drivers' championship aspirations hanging by a thread, but Whitmarsh has vowed his team will respond to Red Bull's charge.
He said: "They looked good, it was the strongest car over the course of the weekend.
"We only had a car capable of the second row in qualifying because Red Bull were quicker.
"We need to look at the car, how we set it up, what developments we can make, the character of the coming circuits and see if we can get back.
"We have had a quick car for a few races but we are in a development race.
"Red Bull look strong, that is the challenge for us and that is the kind of challenge we like to try and respond to."
Suzuka also saw Hamilton involved in an entertaining battle with his 2013 replacement Sergio Perez.
The Sauber driver looked eager to prove a point and slotted past Hamilton with a spectacular late-braking move at the hairpin.
But when he tried to go around the outside of the Briton at the same corner a few laps later, as Hamilton moved to the inside to defend, he could not keep control of his Sauber and spun off into the gravel.
Hamilton described Perez's driving as "crazy" but Whitmarsh was pleased by the Mexican's intent and reiterated his confidence of putting the 22-year-old in a position to win races from the off in 2013.
He said: "I thought he was quite keen, the first move was quite a good move, the second less good.
"But it shows we have someone who wants to go out there and race and challenge. There is a diamond that needs to be honed there and that is quite an interesting challenge."
He added: "We aim to be in with a shout of winning the championship next year.
"We just have to do the best job we can, develop the car, we are making some reasonable progress on next year's car and the aim is to be competitive from the first race."