Ellis and Langridge, who won Olympic bronze last summer, lost 21-18 21-18 to Taiwan's Jhe-Huei Lee and Yang Lee.
Ellis progressed in the mixed doubles alongside Lauren Smith, while Chris and Gabby Adcock also advanced.
Smith earlier teamed up with Sarah Walker to reach the second round of the women's doubles.
Rio Olympic medallists Marcus Ellis and Chris Langridge suffered defeat in the first round of the India Open on a mixed day for English players.