Allardye was captured on camera calling Roy Hodgson "Woy", a nickname mocking his speech impediment, in an undercover report in 2016 that led to the then-England manager Allardyce losing his job.
Hodgson, who managed the English national team before Allardyce's brief stint as head coach, said that he had not yet received any apology from the Everton manager. He went on to say that it was now too late for him to get one.
Speaking in the run-up to Crystal Palace's league clash with Everton, Hodgson stated: "Do you like being insulted? No, not particularly. Did it bother me? I didn't lose any sleep over it.
"My relationship with him before, I always thought was good. Now I would expect it to be less good.
"Would I like him to apologise? No. It's far too late. It has gone. It belongs to the distant past.
"In jobs like I am doing at the moment when you are the manager of a Premier League club, you live very much in the ultimate present and the future.
"I'm not interested. I've said what I've got to say."
Hodgson will be out for revenge when his side travels to Goodison Park on Saturday, as they fight to stay out of the relegation zone. However, they will be without key player Wilfried Zaha, who could be out for a month with a knee injury.