The 24-year-old arrived with high hopes after reaching the Nottingham final last month and then knocking out Caty McNally on Monday for her first win at a grand slam and a likely place in the top 100.
But she found herself staring down the barrel of a humiliating 'double-bagel' in the second round after dropping the first set without winning a game.
Burrage recovered her composure in the second set but Russian Kasatkina, the Eastbourne finalist and 11th seed, proved too strong in a resounding 6-0 6-2 victory.
The British number two was bound to be nervous on her first appearance on Centre Court, and unfortunately it showed.
She won just three points in the opening four games, double-faulting three times to give Kasatkina a 4-0 lead.
Burrage brought up a break point in the next but a slip on the baseline proved costly and before she knew it the first set was over in 19 chastening minutes.
Kasatkina held again at the start of the second before Burrage finally got on the board, raising her arms in mock celebration in front of David Beckham in the Royal Box.
Bear Grylls, also watching from the posh seats, would have enjoyed the survival skills on display as Burrage went on to clinch a break of serve to lead 2-1.
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