The unseeded Indo-Serbian pair lost 3-6 4-6 2-6 to the Argentine team, on Wednesday.
Mankad had entered the main draw through qualifiers and had become the latest Indian player to earn a berth in a major tennis event.
The men's doubles event had five Indian players competing with different partners.
The match between Indian Davis Cuppers -- Somdev Devvarman and Rohan Bopanna -- and their partners was cancelled on Tuesday and will be played on Wednesday.
Somdev and Philippines' Treat Conrad Huey have also qualified for the main draw while Bopanna and Pakistan's Aisam-ul-Haq Qureshi got a direct entry.