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McLaren are to undertake a review of all processes and procedures in the wake of Sunday's disappointing Bahrain Grand Prix.
Lewis Hamilton could only manage eighth after starting second on the grid, the 27-year-old undone by two wretched pit stops.
As for team-mate Jenson Button, the 32-year-old finished outside the points for the second time this season after first suffering a puncture and then a cracked exhaust, forcing him to retire one lap from home.
After heading into the race first and second in the championship, Hamilton now trails race winner Sebastian Vettel by four points, whilst McLaren have fallen behind Red Bull in the constructors'.
"We weren't quick enough, we made mistakes and we had a failure on Jenson's car, so it was a pretty bad day," said Whitmarsh.
"We'll review lots of things, the equipment, the process, the approach because this race was so disappointing."
In particular, Whitmarsh had to relieve the left-rear gunman of his duties during the race as it was he who played a role in both of Hamilton's slow pitstops.
In China last week, Button was denied a shot at victory by a slow final change of tyres as the left wheel nut cross-threaded at the first time of asking.
Yesterday, at Hamilton's first stop, the drive pegs failed to align, and at the second there was another cross-thread, both of which cost Hamilton time and track position.
It left Whitmarsh to have a consoling word with his employee as he said: "We had to change him because he was very stressed.
"But I hope none of us focus on an individual who was very brave to put himself up for what is a difficult, challenging position.
"He's taken it very badly, but I've given him the reassurance and support of this team."
A frustrated Hamilton added: "By rights we should have been fighting to finish in the top four, but it didn't work out like that in the end.
"The delays in the pits were a big part of that. For the driver sitting in the car that's always frustrating because you're just waiting and there's nothing you can do to help.
"I don't know who the guy is, but I will go and see him, try and lift him up."
As for Button, he was left to describe his race as "a disaster", one that has left him 10 points behind Vettel.
It was the 24-year-old's 21st career win, the German ahead of Lotus duo Kimi Raikkonen and Romain Grosjean, with Red Bull team-mate Mark Webber fourth for the fourth consecutive race.
"It was an incredible race. Extremely tough," said Vettel after becoming the fourth different victor this year, a scenario not seen in F1 since 2003.
"We will have a good time now and then push harder so that we are there again in the next race.
"But it's a very tight season, cars are very close to each other and small things can make a huge difference on a Sunday."
Webber trails Vettel by just five points with Mercedes' Nico Rosberg fifth and Paul di Resta sixth in his Force India after adopting a two-stop strategy in comparison to three for those around him.