The Woking-based outfit's run of 64 consecutive points scoring finishes came to an end in Montreal with neither Jenson Button nor Sergio Perez able to get inside the top ten.
That poor performance highlighted the amount of improvement that McLaren still has to make before it can hope of challenging at the front, but Whitmarsh says the outfit must not give up on 2013.
"You have to be an optimist in this business, particularly in these moments, and I've been through various ones before," said Whitmarsh.
"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."
Whitmarsh added that there was some added pressure on McLaren to unlock something from its car for its home race at Silverstone.
"Obviously we want a much better showing at Silverstone," he said. "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."
Whitmarsh was also adamant that the team's stalled form this season was not linked to the loss of Lewis Hamilton, who switched to Mercedes over the winter.
"No, I don't think so. Lewis is a great driver, an asset, and we haven't got him," he said.
"But both of our drivers are doing a good job. We didn't quite get it right between us in qualifying, and as for the race I can be very critical - self critical - in what we should have done.
"No-one expected the prime tyre to do what it did in this race."