It has outscored Force India by 28 points to two over the past three races, so McLaren appears to have taken the decisive upper hand in the battle for fifth.
But with fourth-placed Lotus 122 points ahead, it is unlikely McLaren will be able to climb any higher, and the focus is now on getting onto the podium for the first time this year.
"We're not really thinking about the championship, we're thinking about getting some results," said Whitmarsh when asked by AUTOSPORT whether McLaren's aspirations in the constructors' championship were now fulfilled.
"What we want to do is to make progress. We were as fast as the Mercedes and one of the Red Bulls [at Spa] and we were faster than one Ferrari.
"We have got to go out there and go for podiums."
UPDATES TESTING ON GRAND PRIX WEEKENDS
While the team's factory resources are now dedicated to its 2014 car, McLaren is continuing to work on upgrades tested largely at the track.
Although this does make the race weekends more difficult, Whitmarsh is confident it is allowing McLaren to become more competitive.
"It's hard on the drivers but you can see on Friday and Saturday we are doing a lot of our aerodynamic development work in full-scale here at the track, which is not the best way of preparing for the race," said Whitmarsh.
"But we are doing that because we are focusing the windtunnel, CFD and aerodynamic development [resources] on future programmes.
"But because we are racers and can't help ourselves, we want to improve and we have made some progress by doing that.
"It's efficient in terms of your development resources, but it's a bit painful to do at race meetings."
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