The 10th seeds and French Open champions lost 7-6(4) 4-6 5-7 to the unseeded Finnish-British combo in exactly two hours on the centre court.
The margin of defeat was quite less with the winners taking 109 points to 104 of the Roland Garros winners, who saved eight of the 11 break points they faced.
With Bopanna's defeat, India's challenge has ended in the prestigious grass court tournament.
Bopanna has already exited from the men's doubles while Sania Mirza has also been knocked out of both the women's doubles and mixed doubles events with her respective partners.
Desai was the best performer among the juniors as she reached the third round in girls singles and the second round in the doubles.
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