Warnock, now in charge at Leeds, believes that whoever gets the job will be unable to repeat their predecessor's success at the club.
He told talkSPORT: "If you fall out with the chairman there's only one winner. I think the writing was on the wall months ago at Spurs. They were hoping to get compensation and Harry was hoping to get the England job.
"It's a difficult scenario. You would have thought a club of that nature would have someone lined up. Having done so well under Harry, finishing fourth twice, they can't now bring someone in and be satisfied with going back to sixth or seventh. They've got to hope they can take the club forward.
"And I can't see how the people they are talking about are going to take it on. I can't see them finishing as high as they did under Harry."