Anderson was the first champion when the tournament moved from Memphis to Long Island in 2018, but he was unable to defend his title last year because of injury.
The two-time Grand Slam finalist double-faulted to lose the tiebreaker in the first set, then was broken in the second by Jung, who had to qualify just to make the main draw.
Also, No. 7 seed Cameron Norrie beat Brian Shi 7-5, 6-3; No. 8 Kyle Edmund defeated Yasutaka Uchiyama 7-5, 6-4; Jordan Thompson swept Ivo Karlovic 6-3, 7-6 (2); Yoshihito Nishioka topped Henri Laaksonen 6-3, 0-6, 6-2; Paolo Lorenzi rallied past Danilo Petrovic 4-6, 6-4, 6-0; Soon Woo Kwon edged Go Soeda 6-2, 6-7 (2), 6-3; and Dominik Koepfer eliminated 2019 runner-up Brayden Schnur 6-4, 6-3.