Eklavya's abilities were far better than any other archer during his time, the story is no secret that he cut his thumb as Gurudakshina. But after that did he blame himself for trusting, Did he ever think that he should have denied it?
Ekalavya didn't blame himself for cutting of his thumb because his guru Dronacharya told him to do it and he had to do it. He also didn't blame himself for doing it because he never had the thought that he did something naive. It says here. Ekalavya likes his guru Dronacharya.
Ekalavya, from what we see of him in the Critical Edition of the Mahabharata, he seems to just do what is told to him. When Dronacharya asks for his thumb as Guru Dakshina, he gives it without any second thoughts. So we can assume that he never wanted to not give his thumb or he never had any second thoughts. He respects his guru, and he did what was told to him. Ekalavya is one who is glad to do anything that his told by his guru, so we can safely assume that he never felt sad that he will never be able to shoot an arrow again.
Source: Critical Edition of Mahabharata (the book).
Vaiśampāyana describes Ekalavya as 'ever devoted to truth' (satye nirataḥ sadā) so it's unlikely he had any regrets later for cutting off his thumb and keeping his promise.
Then Drona, O king, addressed Ekalavya, saying,
If, O hero, thou art really my pupil, give me then my fees.
On hearing these words, Ekalavya was very much gratified, and said in reply,
O illustrious preceptor, what shall I give? Command me; for there is nothing, O foremost of all persons conversant with the Vedas, that I may not give unto my preceptor.
O Ekalavya, if thou art really intent on making me a gift, I should like then to have the thumb of thy right hand.
Vaisampayana continued, 'Hearing these cruel words of Drona, who had asked of him his thumb as tuition-fee, Ekalavya, ever devoted to truth and desirous also of keeping his promise, with a cheerful face and an unafflicted heart cut off without ado his thumb, and gave it unto Drona. After this, when the Nishada prince began once more to shoot with the help of his remaining fingers, he found, O king, that he had lost his former lightness of hand. And at this Arjuna became happy, the fever (of jealousy) having left him...'
Interestingly, in a similar conversation between Paraśurāma (guru) and Bhīṣma (śiṣya), Bhīṣma rejects Paraśurāma's demand that he marry Ambā saying Paraśurāma is unacquainted with the conduct of a guru:
Then Rama [Paraśurāma] answered me with eyes red in anger,
Thou knowest me, O Bhishma, to be thy preceptor, and yet, O Kauravya, thou acceptest not, for pleasing me, this daughter of the ruler of Kasi! O delighter of the Kurus, I cannot be gratified unless thou actest in this way! O mighty-armed one, take this maiden and preserve thy race! Having been abducted by thee, she obtaineth not a husband.
Unto Rama that subjugator of hostile cities, I [Bhīṣma] replied, saying.--
This cannot be, O regenerate Rishi! All thy labour is vain, O son of Jamadagni, remembering thy old preceptorship, I am striving, O holy one, to gratify thee! As regards this maiden, she hath been refused by me before knowing what the faults, productive of great evils, of the female sex are, who is there that would admit into his abode a woman whose heart is another's and who (on that account) is even like a snake of virulent poison? O thou of high vows, I would not, even from fear of Vasava, forsake duty! Be gracious unto me, or do me without delay that which thou hast thought proper. This sloka also, O thou of pure soul, is heard in the Puranas, O lord, sung by the high-souled Marutta, O thou of great intelligence! The renunciation is sanctioned by the ordinance of a preceptor who is filled with vanity, who is destitute of the knowledge of right and wrong, and who is treading in a devious path.
Thou art my preceptor and it is for this that I have from love reverenced thee greatly. Thou, however, knowest not the duty of a preceptor, and it is for this that I will fight with thee. I would not slay any preceptor in battle, especially again a Brahmana, and more specially one endued with ascetic merit. It was for this that I forgive thee.