pasparśa pādayor enaṁ
Indra was very ashamed of having offended the Lord. Approaching Him in a solitary place, Indra fell down and lay his helmet, whose effulgence was as brilliant as the sun, upon the Lord’s lotus feet.
The specific “solitary place” where Indra approached Śrī Kṛṣṇa is mentioned by the sage Śrī Vaiśampāyana in the Hari-vaṁśa (Viṣṇu-parva 19.3): sa dadarśopaviṣṭaṁ vai govardhana-śilā-tale. “He saw Him [Kṛṣṇa] sitting at the base of Govardhana Hill.”
From the commentaries of the ācāryas we understand that Lord Kṛṣṇa wanted to provide a solitary meeting for Indra so that he would not be further humiliated. Indra came to surrender and beg forgiveness, and the Lord allowed him to do so privately.