Despite overwhelming support at Silverstone for home heroes Lewis Hamilton and Jenson Button, the McLaren duo trailed in eighth and 10th behind Red Bull's Mark Webber.
Disappointingly for Whitmarsh, his team has now slumped to fourth in the constructors' championship behind Red Bull, Ferrari and Lotus, a position the Woking-based marque are unaccustomed to.
Hamilton and Button were hopelessly off the pace, leaving them 37 and 79 points adrift in the championship standings respectively, with Fernando Alonso's lead cut to 13 by Webber.
It is hard to believe just over four weeks ago McLaren were celebrating a Hamilton victory in Montreal that edged him back in front in the title race.
Now, according to Button, they were only the sixth quickest team at Silverstone having also fallen behind Williams and Sauber in terms of pace.
"It's tough, but we've been through all sorts of highs and lows as a team, and we're resilient enough," said Whitmarsh.
"But the drivers know, and we know, we need to work on the car, make it better, understand the tyres. Those are the things that are part of our job.
"So we'll be pushing hard. I don't think we need to build morale, everyone is going to be pretty focused to try and achieve that.
"At this time I'm not seriously worried. Being worried doesn't make the car go quicker. Of course I'm disappointed, but there's no magic."
Whitmarsh has vowed a more visible upgrade package will be on the cars for the German Grand Prix at Hockenheim on July 22, notably pertaining to the top body at the rear.
However, he can offer no promises as to its performance, adding: "Anyone who makes predictions this season is very rash.
"Everyone knows this team is strong and committed to winning, and the drivers and team will be giving it their all. We'll see what we can do when we get to Germany.
"It's a decent upgrade, although I'm sure no-one is going to stand still and wait for us. You have to do a good job.
"We've been flat out as we always are. We're trying to pull them (the upgrades) through as quick as we can."
For Whitmarsh, the Pirelli tyres continue to remain a mystery, as witnessed with Hamilton on Sunday. He used two sets of the same hard compound, each reacting differently.
"It is very tricky to go from being so strong in the first stint on one set of prime (hard tyres), then about 15 minutes later you put them on again and they feel different," said Whitmarsh.
"They responded differently, yet we set the same pressures and temperatures, so we have to understand them better because if you can get them working you can be a second up, as we've seen."