Allardyce became the eighth managerial change of the Premier League season earlier this week.
"I sympathise with Sam. It's absolutely crazy," the Irishman told Villa's website.
"If you were put into a job in the city and asked to turn things around and someone thought enough of you to be able to do it, the first thing you'd ask for is time.
"You'd say 'This won't change overnight' and 'You can't wave a magic wand'. Everyone would give that particular person time to do the job.
"But with football, it's absolutely out of hand. It's so crazy now.
"When I was a player, managers were getting sacked but they were getting two years in the job. Now it's two minutes.
"In Sam's few months at Newcastle he might not even have found out the correct strength of the reserve side. He might have players injured that he doesn't know much about.
"I know that from my experience at Leicester, Celtic and even here. The minute you come in, you're in charge.
"The players don't know you and it takes a while to gel. You don't get time in football. It's done for. There is no such thing.
"I'd love to say I have a five-year plan or ideas for the youth team. Have a bit of sense - it just doesn't happen."