The Briton was in brilliant form at Spa as he delivered the first lights-to-flag victory of the 2012 Formula 1 season.
And although Button is still 63 points adrift of points leader Fernando Alonso, Whitmarsh thinks there is no doubt that the 2009 world champion can build on his success and set his sights on the title once again.
"He was frustrated when things didn't go well, but I think with a performance like that he's got to believe that he is capable of getting up there now," said Whitmarsh. "It's a long old season to go.
"Clearly we've got a quick car. We've been quick on both sides of the break on very different circuits and that must be reassuring for him. It must give him the confidence that he can really get the job done.
"I think people quickly get on the case of loss of form, but actually I think he always believed in himself."
Although Button's team-mate Lewis Hamilton had a more difficult weekend - both on and off track Whitmarsh sees no evidence to suggest that his title efforts are stalling.
"It has been a difficult week for Lewis, but he is actually very tough and he's starting to be a seasoned campaigner," he said. "I would not be surprised if he doesn't come back super strong and win in Monza.
"Now both drivers and the whole team will be focused on that and the races ahead of that."