Remembering Gajendra Moksha narration is most beneficial for all who are performing Kartik-vrata. It is written here in the importance of Gajendra Moksha narration that listening to these prayers will benefit the votary even if he is not able to understand the meaning. Listening to the prayers of Gajendra, the Lord Himself came in person and rescued him. Actually, the Lord does not require to come in person to rescue anyone but to give satisfaction to Gajendra He comes in person being seated on Garuda. The Supreme Lord wants to reach His devotee so rapidly that even the speed of Garuda, He felt less and He dismounted Himself from Garuda and rushed to Gajendra.

The Lord got satisfied by the prayers of Gajendra. If we can recite these prayers with the same earnestness and feelings as Gajendra then we should also get the grace of Supreme Lord. But we are unable to do so.

śrī-gajendra uvāca
oṁ namo bhagavate tasmai
yata etac cid-ātmakam
puruṣāyādi-bījāya
pareśāyābhidhīmahi

yasminn idaṁ yataś cedaṁ
yenedaṁ ya idaṁ svayam
yo ’smāt parasmāc ca paras
taṁ prapadye svayambhuvam

yaḥ svātmanīdaṁ nija-māyayārpitaṁ
kvacid vibhātaṁ kva ca tat tirohitam
aviddha-dṛk sākṣy ubhayaṁ tad īkṣate
sa ātma-mūlo ’vatu māṁ parāt-paraḥ

kālena paṣcatvam iteṣu kṛtsnaśo
lokeṣu pāleṣu ca sarva-hetuṣu
tamas tadāsīd gahanaṁ gabhīraṁ
yas tasya pāre ’bhivirājate vibhuḥ

na yasya devā ṛṣayaḥ padaṁ vidur
jantuḥ punaḥ ko ’rhati gantum īritum
yathā naṭasyākṛtibhir viceṣṭato
duratyayānukramaṇaḥ sa māvatu

didṛkṣavo yasya padaṁ sumaṅgalaṁ
vimukta-saṅgā munayaḥ susādhavaḥ
caranty aloka-vratam avraṇaṁ vane
bhūtātma-bhūtāḥ suhṛdaḥ sa me gatiḥ

na vidyate yasya ca janma karma vā
na nāma-rūpe guṇa-doṣa eva vā
tathāpi lokāpyaya-sambhavāya yaḥ
sva-māyayā tāny anukālam ṛcchati

tasmai namaḥ pareśāya
brahmaṇe ’nanta-śaktaye
arūpāyoru-rūpāya
nama āścarya-karmaṇe

nama ātma-pradīpāya
sākṣiṇe paramātmane
namo girāṁ vidūrāya
manasaś cetasām api

sattvena pratilabhyāya
naiṣkarmyeṇa vipaścitā
namaḥ kaivalya-nāthāya
nirvāṇa-sukha-saṁvide

namaḥ śāntāya ghorāya
ghūḍhāya guṇa-dharmiṇe
nirviśeṣāya sāmyāya
namo jñāna-ghanāya ca

kṣetra-jñāya namas tubhyaṁ
sarvādhyakṣāya sākṣiṇe
puruṣāyātma-mūlāya
mūla-prakṛtaye namaḥ

sarvendriya-guṇa-draṣṭre
sarva-pratyaya-hetave
asatā cchāyayoktāya
sad-ābhāsāya te namaḥ

namo namas te ’khila-kāraṇāya
niṣkāraṇāyādbhuta-kāraṇāya
sarvāgamāmnāya-mahārṇavāya
namo ’pavargāya parāyaṇāya

guṇāraṇi-cchanna-cid-uṣmapāya
tat-kṣobha-visphūrjita-mānasāya
naiṣkarmya-bhāvena vivarjitāgama-
svayaṁ-prakāśāya namas karomi

mādṛk prapanna-paśu-pāśa-vimokṣaṇāya
muktāya bhūri-karuṇāya namo ’layāya
svāṁśena sarva-tanu-bhṛn-manasi pratīta-
pratyag-dṛśe bhagavate bṛhate namas te

ātmātma-jāpta-gṛha-vitta-janeṣu saktair
duṣprāpaṇāya guṇa-saṅga-vivarjitāya
muktātmabhiḥ sva-hṛdaye paribhāvitāya
jñānātmane bhagavate nama īśvarāya

yaṁ dharma-kāmārtha-vimukti-kāmā
bhajanta iṣṭāṁ gatim āpnuvanti
kiṁ cāśiṣo rāty api deham avyayaṁ
karotu me ’dabhra-dayo vimokṣaṇam

ekāntino yasya na kañcanārthaṁ
vāñchanti ye vai bhagavat-prapannāḥ
aty-adbhutaṁ tac-caritaṁ sumaṅgalaṁ
gāyanta ānanda-samudra-magnāḥ

tam akṣaraṁ brahma paraṁ pareśam
avyaktam ādhyātmika-yoga-gamyam
atīndriyaṁ sūkṣmam ivātidūram
anantam ādyaṁ paripūrṇam īḍe

yasya brahmādayo deva
vedā lokāś carācarāḥ
nāma-rūpa-vibhedena
phalgvyā ca kalayā kṛtāḥ

yathārciṣo ’gneḥ savitur gabhastayo
niryānti saṁyānty asakṛt sva-rociṣaḥ
tathā yato ’yaṁ guṇa-sampravāho
buddhir manaḥ khāni śarīra-sargāḥ

sa vai na devāsura-martya-tiryaṅ
na strī na ṣaṇḍho na pumān na jantuḥ
nāyaṁ guṇaḥ karma na san na cāsan
niṣedha-śeṣo jayatād aśeṣaḥ

jijīviṣe nāham ihāmuyā kim
antar bahiś cāvṛtayebha-yonyā
icchāmi kālena na yasya viplavas
tasyātma-lokāvaraṇasya mokṣam

so ’haṁ viśva-sṛjaṁ viśvam
aviśvaṁ viśva-vedasam
viśvātmānam ajaṁ brahma
praṇato ’smi paraṁ padam

yoga-randhita-karmāṇo
hṛdi yoga-vibhāvite
yogino yaṁ prapaśyanti
yogeśaṁ taṁ nato ’smy aham

namo namas tubhyam asahya-vega-
śakti-trayāyākhila-dhī-guṇāya
prapanna-pālāya duranta-śaktaye
kad-indriyāṇām anavāpya-vartmane

nāyaṁ veda svam ātmānaṁ
yac-chaktyāhaṁ-dhiyā hatam
taṁ duratyaya-māhātmyaṁ
bhagavantam ito ’smy aham
(Srimad Bhagavatam 8.3.2-29)

Gajedra is praying with humility, “Your devotees are always immersed in bliss derived from singing Your glories. One who has the wealth of surrendered unto You never asks for anything else. But being an animal I do not have such eligibility. You can give everything—dharma (piety); artha (wealth); kama (fulfillment of desires); moksa (salvation). You can award transcendental body. You can also award Your abode and loving devotion unto You. I do not have eligibility for all these. What should I do? You please rescue me from the clutches of crocodile.”

Though externally he is praying this but from within he is desirous of getting Lord’s abode and loving devotion but he feels himself ineligible to ask for those attainments. He has humility in his heart because of which he said that he is not hoping to get those attainments and praying for the deliverance from the clutches of the crocodile.