The 70-year-old Yorkshireman met chairman Mehmet Dalman and chief executive Ken Choo for talks on Monday when it was agreed that he would continue in a job he has held since October 2016.
"When you get relegated the manager's position is usually in doubt," Warnock said.
"But Vincent (Tan, Cardiff owner) made it clear last week that he wanted me to stay, and how can you not want to when you see how the fans have been with me over the last couple of years?
"It rankles a little bit that we got relegated. I just feel it's not the time to change with the squad I've got and the players I want to bring in.
"But we've got to obviously look for a replacement for me now.
"I would like to think we could do well and I can help them in that selection."
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