SB 10.27.2

vivikta upasaṅgamya
 vrīḍītaḥ kṛta-helanaḥ
pasparśa pādayor enaṁ
vivikte — in a solitary place; upasaṅgamya — approaching; vrīḍitaḥ — ashamed; kṛta-helanaḥ — having committed offense; pasparśa — he touched; pādayoḥ — upon His feet; enam — Him; kirīṭena — with his helmet; arka — like the sun; varcasā — the effulgence of which.
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.