Indra is deceptive by nature and, generally, his words should not be taken at face value.
Still, he is technically right that it is impossible to become a Brahmana by penance (tapas). That can be seen Yakṣa Praśna, where Yudhiṣṭhira says
The Yaksha asked,—“By what, O king, birth, behaviour, study, or learning doth
a person become a Brahmana? Tell us with certitude!” Yudhishthira answered,-
“Listen, O Yaksha! It is neither birth, nor study, nor learning, that is the cause of Brahmanahood, without doubt, it is behaviour that constitutes it. One’s behaviour
should always be well-guarded, especially by a Brahmana. He who maintaineth his
conduct unimpaired, is never impaired himself. Professors and pupils, in fact, all who study the scriptures, if addicted to wicked habits, are to be regarded as illiterate wretches. He only is learned who performeth his religious duties. He even that hath studied the four Vedas is to be regarded as a wicked wretch scarcely distinguishable from a Sudra if his conduct be not correct. He only who performeth the Agnihotra and hath his senses under control, is called a Brahmana!”
From that, it can be implied that yajña, not tapas, is needed to become a Brahmana and Indra is just being unhelpful not pointing it out.
Basically, it is like the saying you can't fill a glass that is already full. You need to sacrifice things (false knowledge, false ideas, senses, wood, etc.)