Scarlett O., here is an example of why people think the Septuagint is quoted by NT authors. This one is not Jesus, but Paul referring to Isaiah 29:14. However, I think it will at least partially show an example of the reasoning people have, though it may not exactly address your question. I have bolded the significant portion.
Isaiah 29:14
KJV translation from the Hebrew OT: Therefore, behold, I will proceed to do a marvellous work among this people, even a marvellous work and a wonder:
for the wisdom of their wise men shall perish, and the understanding of their prudent men shall be hid.
Brenton translation from the Greek OT: Therefore behold I will proceed to remove this people, and I will remove them: and
I will destroy the wisdom of the wise, and will hide the understanding of the prudent.
1 Corinthians 1:19
KJV translation of Greek NT: For it is written,
I will destroy the wisdom of the wise, and will bring to nothing the understanding of the prudent.
1 Corinthians 1:19
Greek text from Brenton OT: διὰ τοῦτο ἰδοὺ ἐγὼ προσθήσω τοῦ μετατεθῆναι τὸν λαὸν τοῦτον καὶ μεταθήσω αὐτοὺς καὶ
ἀπολῶ τὴν σοφίαν τῶν σοφῶν καὶ τὴν σύνεσιν τῶν συνετῶν κρύψω.
Greek text from [see below]: γέγραπται γάρ
ἀπολῶ τὴν σοφίαν τῶν σοφῶν καὶ τὴν σύνεσιν τῶν συνετῶν ἀθετήσω
It is not necessary in this example to be able to read to read the Greek with understanding to see that the characters of the NT Greek text duplicates the Septuagint Greek text. There is no question about that. One cannot argue that they do not match. The argument then that folks are making is about the how and why. For example (1) Paul quotes the Septuagint; or (2) Origen back-translated the Septuagint to match Paul's statement. I am not going to get into that argument, but what is above is an easy example to see that the Greek NT of this verse matches the Septuagint, at least as it has been preserved to the present.
[Note: Greek in
1 Corinthians 1:19 appears to be the same in 1550 Stephanus, 1881 Westcott-Hort, 1894 Scrivener, 2010 SBL, and 2017 Tyndale House, per Bible Gateway, except for superficial differences in markings, capitalization, and punctuation. So this should not be a question of variant texts here.]