Gojo Satoru's death in Jujutsu Kaisen was quite an unfortunate development. While there were hints that he would be sidelined from the story, almost no one expected it to be in this manner. However, creator Gege Akutami had his reasons, and the white-haired sorcerer had to pass on the torch to the next generation for the story to fully progress.
That aside, Gojo did leave his students with something as he departed. For Megumi, it was informing him that he had been the one to kill Toji. For Nobara, Gojo left her mother's whereabouts, possibly wanting to seek her out. But there was nothing left behind for Yuji. Instead, he had personally spoken to him before the final showdown, which defined their relationship in the series.
Jujutsu Kaisen: Gojo's parting words epitomize their bond

Before he descended into battle with Ryomen Sukuna, Gojo bid farewell to the remaining members of Jujutsu High. These included characters like Yuta Okkotsu, Maki Zenin, Atsuya Kusakabe, Principal Gakuganji, Utahime Iori, and others. For Yuji, however, Gojo had had a personal conversation with him. Although a brief one, it perfectly laid out what their bond stood for in Jujutsu Kaisen.
To begin with, Gojo asked Yuji to be forward-thinking, to look beyond himself and develop a strength of his own. This power would be completely different from the known Gojo Satoru's power, which carries on in the event of his death. While none of his students would forget him, he wanted to grow to be sorcerers of their own kind, ones who surpass him and keep moving forward.
Gojo saying "I'm expecting great things of you" to Yuji speaks of how highly he views the boy. After all, he did oppose and delay the teenager's execution. He was even willing to go against the authorities to keep Yuji alive, not because he saw the pink-haired teen as a vessel to contain Sukuna, but because he saw Yuji Itadori for who he was.

Although flawed, the boy always looked out for those he cared about and highly valued Life. He was, by no means, perfect, but that is what made him special. Under Gojo's tutelage till his death, Yuji learned what it meant to be a sorcerer. From Cursed Energy to Domain Expansions, Gojo was there with the boy through it all. Gojo’s mentorship was deeper than just combat training.
He wanted to instill in Yuji a philosophy that underpins the series. Moral ambiguity was to be questioned, and life was important in a chaotic world. Gojo didn't conceal the horrors of being a sorcerer, but ensured that Yuji focused on the greater picture— protecting others, even if it means giving up one's own peace, distinguishing the strong from the honorable.
When looked at closely, Gojo's final words to Yuji in Jujutsu Kaisen weren't merely a farewell, but a rite of passage. This was where the student stepped forth as the teacher stepped down. Not answers, but expectations to be great, that was what Gojo left with the teen, i.e., faith in a dark world. Given how fleeting it was, faith was invaluable to one like Yuji, who was battling his demons of identity and role.
In conclusion

Gojo Satoru’s demise in Jujutsu Kaisen was pivotal in the series— emotionally heavy and narratively necessary. Although devastating, it shifted the spotlight onto the new generation of sorcerers. Specifically, before his death, Gojo's exchange with Yuji highlighted how deep their bond ran. Nothing tangible, but Gojo left Yuji with Belief. This was a crucial gift in a world plagued by Curses and moral decay.
Besides Jujutsu, Gojo passed on his ideals and dreams to the boy, imparting that it lay in purpose and not simply power. Given Yuji's predicament with his battle of self-worth and Sukuna within him, faith was something he badly needed. Gojo's final lesson was simple— be more than is expected of you, and protect, no matter what it takes.
Related links:
- Gege drops the saddest Yuji-Gojo parallel in Jujutsu Kaisen yet, and it has to do with Megumi Fushiguro
- Gojo has always put Yuji before Megumi (and Jujutsu Kaisen chapter 229 confirms it)
- Gojo did tell Yuji about his parents in Jujutsu Kaisen (& Megumi and Nobara's letters prove it)