• alabdha - maṇiḥ — having not obtained the jewel
  Compound: a-labdha (not obtained) + maṇi (gem). The verse opens on a negation — Bhagavān is named by what He has not found. Gauḍīyas read this as deliberate self-effacement: the īśvara consents to be the one without.
• agra - ja — elder brother
  Compound: agra (front, prior) + ja (born). Standard kinship term for elder brother; here it foregrounds the dāsya-bhāva Kṛṣṇa shows to Balarāma even in His Dvārakā kṣatriya register. Gauḍīyas treat agraja as a doctrinal hinge for the brothers' rasa-relation.
• vṛthā hataḥ — uselessly killed
  Adverb vṛthā (in vain) + past participle of √han. Bhagavān admits the act looks futile. Bhāgavata's confidence in His readers: He stages futility because the next verse, in Balarāma's mouth, will resolve it.
• na vidyate — is not present, does not exist
  Present passive of √vid (to find / be). The verse closes on absence — the jewel 'is not found.' Gauḍīyas note the philosophical resonance: Bhagavān can speak even the language of 'na vidyate' when the līlā calls for it.

• Where could honest admission that 'we didn't get what we came for' be part of a real campaign?
• How does the Lord's frankness model your own debriefs?

Kṛṣṇa returns to Balarāma empty-handed and admits — 'vṛthā hataḥ,' uselessly killed. Even Bhagavān can speak in the register of frustrated investigation. The verse is one of the Bhāgavata's gentlest demonstrations that omniscience consents to play the role of a man with empty hands.