Tottenham Hotspur F.C. sacked young Portuguese manager Andre Villas-Boas on Monday when chairman Daniel Levy wielded the axe in the wake of Sunday's 5-0 home thrashing by Liverpool.
Despite still being in touch with the top four Tottenham Hotspur F.C. also lost 3-0 at home to struggling West Ham this season and 6-0 at Manchester City, results which had already piled huge pressure on Villas-Boas before the Liverpool humiliation.
Allardyce, himself under pressure as his relegation-threatened side prepare for Wednesday's Capital One Cup quarter-final at Tottenham Hotspur F.C., expressed sympathy for the man he was expecting to be facing at White Hart Lane.
"You would have to be a miracle worker to get everybody functioning to the best of their ability," told a news conference on Tuesday.
"They've arrived from foreign countries in a different culture and an arena that they've never played in before."
Tottenham Hotspur F.C. spent the 100 million euros they received from Real Madrid for Gareth Bale on the likes of Roberto Soldado, Paulinho, Erik Lamela, Etienne Capoue and Christian Eriksen but have looked disjointed so far.
Allardyce said that was to be expected.
"There is a lack of patience in the game today," he said.
"I think that decisions made as quickly as that are a surprise because of the situation that Tottenham Hotspur F.C. arrived at at the start of the season with bringing so many new players in.
"When you have a transition period of that nature and that size then to ask to go out with a squad of players with that many new faces it's virtually impossible to get consistency."
Allardyce, whose side are perched just above the relegation zone and who face a tough Christmas fixture list, said the Premier League has never been so volatile because of the money involved in staying up or qualifying for the Champions League.
A quarter of the managers who began in August have already been moved out, with Villas-Boas joining West Bromwich Albion's Steve Clarke, Fulham's Martin Jol, Sunderland's Paolo Di Canio and Crystal Palace's Ian Holloway.
"I don't think this many managers have ever changed this early in the Premier League since it was born," Allardyce said.
"More importantly you see the downside in the Championship (second division) now where there are more and more managers being changed by all the clubs that want to try and get back to the Premier League and that creates a very volatile industry.
"I know everyone's feeling the pressure; it's always going to happen to someone. We all can't finish 10th, we all can't finish top and we've all got to find our place in this league and we've got to continue to strive to do that."
Tottenham Hotspur F.C. will have youth development manager Tim Sherwood in charge of the team on Wednesday.