Bhambri, who recently beat French World number 22 Gael Monfils, suffered a 6-1 1-6 3-6 defeat at the hands of 22nd seed Japanese in the opening round, which lasted one hour and 44 minutes.
The left-handed Prajnesh, who has been named in Indian Davis Cup team as a reserve, lost 1-6 4-6 to Germany's Yannick Hanfmann in his first round match.
India's hopes to see a singles player competing in the main draw of the last Grand Slam of the season still remained alive with Ramkumar Ramanathan featuring in the bottom half of the qualifying draw.
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