"People demand success and they demand it very quickly," said Jefferies who stood down at Kilmarnock in January after nearly eight years at the helm.
"It's a great achievement now to be at a club two years."
Since the end of last season there has been managerial change at eight of the 12 clubs in the Scottish Premier League.
Jefferies was not out of work for long, with the 59-year-old making a dramatic return to Tynecastle, just two hours after they sacked Csaba Laszlo.
The bigger picture is the league's too tight
Asked if he could see another manager lasting as long as he did at Rugby Park, Jefferies said: "I cannot see that happening too often.
"You'll be one of a very, very small band if you manage to last eight years.
"I can look back on that and say that was an achievement in itself."
Jefferies, who spent five years as Falkirk boss in the early 1990s, expressed sympathy for May but felt he was on a hiding to nothing after stepping up from the youth team for his first job in management.
"Jumping from what Eddie was at youth level right up to a manager was always going to be tough," said Jefferies, who thought May could have benefited from learning his trade in the lower leagues.
"But I'm sure he'll have gained a lot of experience in his short time there which will help him."
Jefferies also had words of warning for May's successor, Steven Pressley, whom he brought to Hearts as a player in 1998 and will face across the dugout at Tynecastle on Saturday.
Admitting the former Scotland defender was management material, he said: "You could see a bit of that in him, the type of boy he was.
"But being a number two and a number one is totally different as well."
Jefferies also thinks that the recent manager casualties demonstrate the need to expand the SPL.
"The bigger picture is the league's too tight," he said.
"You look at some of these clubs in the First Division, like Dunfermline.
"We should get away from playing each other four times.
"With Rangers and Celtic, when it first started, we were getting two gates and everybody was in favour of that because of the big crowds. That doesn't happen anymore.
"All you do is get more change of managers and there's no breathing space for younger players coming through as well."
Source: BBC Sport