The sixth-seeded pair of Bopanna and Roger-Vasselin went down 4-6, 4-6 to the 12-seeded British duo in the third round on Sunday.
However, other Indian tennis players Leander Paes and Sania Mirza entered the quarter-finals of their respective categories in the US Open.
While the veteran Paes won his men’s doubles tie with Czech partner Radek Stepanek, Sania advanced with China’s Jie Zheng in the women’s doubles.
Seeded fourth, Paes and Stepanek won 7-5, 4-6, 6-3 against French 14th seeds Michael Llodra and Nicolas Mahut in two hours and 12 minutes on Court 17.
After sharing the first two sets, the fourth seeds converted their only breakpoint in the deciding set to bag the match.
Elsewhere on Court 8, 10th seeds Sania and Jie Zheng upset German-Czech sixth seeds Anna-Lena Groenefeld and Kveta Peschke 6-2, 6-3 in one hour and 12 minutes to enter the last eight.
The triumphant team converted two breakpoints in each set to easily win the third round rubber.