The 29-year-old was excluded from Spurs' 25-man squad submitted on Thursday, despite injured players Xavi Simons and Wilson Odobert being included.
Richarlison's omission followed a turbulent week in which De Zerbi revealed that the former Everton striker had asked to leave the club. He came close to returning to Everton before Tuesday's transfer deadline, but the proposed move collapsed.
Turkish side Trabzonspor had also been linked with Richarlison before their transfer window closed on Friday evening. Saudi Arabian clubs, however, can still make signings until Sunday.
"It was not my decision. It is the normal decision," said the Italian boss.
"I think Richarlison, he decided everything alone. He spoke with me at the beginning of the pre-season and told me his idea and desire was to leave.
"At the end we go to bring another striker [in] and like I said at the beginning of the pre-season, I want to keep the players, just the players that want to stay and be proud and with the right passion to stay here.
"Then for everything and other problems, it is not my business and not my job. It is the responsibility of the club.
"I can't say nothing because I didn't decide anything. The message of Richarlison from the beginning of the season has been very clear. I accepted that and for me [there is] nothing [to say]."
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