Whitmarsh is presiding over one of McLaren's leanest periods since he took charge of the team early in 2009, with just 37 points taken from the opening seven races.
McLaren are already 164 points down on Red Bull in the constructors' championship, and are in such a slump they also trail Force India.
The team's woes are such that even Jenson Button has given up on any hope he had of winning this year's world title.
That followed an abysmal Canadian Grand Prix in which McLaren failed to score a point for the first time since the final race of 2009, bringing to an end their record run of 64 races in the points.
Ahead of the team's home race at Silverstone on June 30, McLaren fans are unlikely to have much to cheer.
But a determined Whitmarsh said: "You have to be an optimist in this business, particularly in these moments, and I've been through various ones before.
"We have to keep people motivated and focused, we have to believe we can work hard and win a race. We haven't given up yet.
"Obviously we want a much better showing at Silverstone, it's important. We want to do that for the fans.
"In a way there is a bit more pressure because you don't want to disappoint people who turn up to support the team.
"So we'll be working hard in the couple of weeks we have now to see what we can do, and pull out, for the British Grand Prix."
Button may have given up hope of the title, but he still hopes to salvage some positives out of this season.
Asked by Press Association Sport whether he was already starting to look towards next term, Button said: "We're so far behind we're not going to win the championship this year. But we can still win grands prix, there is still that possibility and you have to aim for that.
"I'm still at a great team, probably the best team to try and fight their way out of this kind of situation. It will happen."
In Montreal, though, McLaren not only turned up with a bad car but failed to even implement a reasonable strategy, admitting to starting Button and team-mate Sergio Perez on the wrong tyre.
Going into the British GP, McLaren could not have produced a worse performance.
"It was another weekend in which we should have done a better job," said Whitmarsh.
"Apart from having a car that wasn't quick enough it was also a weekend where everything didn't fall into place.
"We should have scored some points, but we weren't fast enough and we didn't plan well.
"What happened is clearly not the result we wanted, but there's no magic, we have to work hard, keep focused and make sure we find a way forward to make the car quicker.
"But looking and standing back from the overall race, we got it wrong in my view.
"It's obviously sad our record for consecutive races in the points is at an end, which is tough, but we don't worry about that.
"We're just frustrated we didn't do a better job."