The Celtic boss has endured a turbulent season, which saw him sent bullets and viable parcel bombs through the post, but is determined to remain at Parkhead next term.
But Smith, who retired as Rangers manager at the weekend, said in the Daily Record: "If any packages had been directed at me then I wouldn't have been in the job any longer.
"I know Neil said that the threats he received, and the packages that had been intercepted by the police before they could reach him, would not drive him out of his job at Celtic.
"But it would have been the end for me. I would not have been in the job any longer. Nothing is worth that just for a game of football."
Smith was spoken to by Strathclyde Police after the threats were made against Lennon.
He added: "I have to admit that visit from the police left me shaken.
"Never in my wildest dreams did I think I'd be sitting at Murray Park one day listening to a policeman tell me what I should instruct my wife to do if anything suspicious arrived at our house.
"I have no time for the sectarian aspect which attaches itself to the Old Firm and neither do my Catholic friends."