Yuki suffered a 4-6 3-6 defeat against Germany's Tim Puetz while Ramkumar Ramanathan was routed 2-6 0-6 by America's Jared Donaldson.
Russian Evgeny Donskoy had ousted Somdev Devvarman 6-2 6-4 in his second round.
The Indian challenge at the second Grand Slam of the season will be led by world number one Sania Mirza in women's doubles.
Rohan Bopanna will play in men's doubles.