Aaron Lennon pounced to give Tottenham a second-minute lead against Roy Keane's men in Saturday's White Hart Lane clash, after calamitous defending from Nyron Nosworthy and Paul McShane.
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Premier League video highlights.Spurs went on to complete a 2-0 victory, withstanding a tremendous second-half fightback from the Wearsiders.
Whitehead, who returned to his usual central midfield slot after a hamstring problem forced out Kieran Richardson, insists that the gifts must be cut out if Sunderland are to get away from the drop zone.
He said: "You can't give teams a head start in the Premier League, especially teams with the quality of players they've got.
"When the ball's there, we've got to clear it rather than mess about, especially in the first 20.
"It's a habit and we need to stop that as soon as possible and start picking up points on the road.
"I don't think it's psychological away from home, we've just got to concentrate for the full 90 minutes."
Sunderland's defeat at Tottenham maintained their dismal record in London – no top-flight league wins in the capital since 2001 – and was their tenth in 12 away games this term, with only two points picked up on the road.
It's the biggest problem for the Wearsiders, whose home record is the best of the bottom six.
But that home record will come under intense pressure in the next two Stadium of Light matches, with relegation rivals Birmingham (January 29) and Wigan (February 9) heading north.
Whitehead added: "We'll get back on the training ground and I'm sure we'll lift ourselves again. Our home form's been good recently, so we're putting a lot of pressure on ourselves to pick up points there."
Saturday's defeat at White Hart Lane saw Sunderland under the cosh for the first half, and lucky to escape being three goals down, but for some inspired goalkeeping by Craig Gordon.
But it was a different scenario in the second half, with the visitors laying siege to the Tottenham goal.
Whitehead said: "We always felt we could get good balls in the box and we got some good headers of the ball. They were scrambling a couple of times in the box, their keeper made a couple of good saves and it wasn't to be.
"Kenwyne is big, strong, quick – he's got the lot.
"He often makes bad balls into good balls.
"We need to get him more support because he does an unbelievable job."
The full article contains 467 words and appears in Sunderland Echo newspaper.