The Portuguese coach was sacked on Monday in the wake of a 5-0 home defeat to Liverpool following 17 months in charge.
Villas-Boas spent heavily in the summer to try to compensate for the sale of star man Gareth Bale to Real Madrid, but with some seven new arrivals at White Hart Lane, Irons boss Allardyce - whose side face Spurs in the quarter-finals of the Capital One Cup on Wednesday night - felt the 36-year-old just needed more time to get things right.
"When you are in a transition period of that nature and that size, with so many new faces, it is virtually impossible to get consistency and arrive at what the expectation is," Allardyce said.
"Decisions made as quickly as that are a surprise because of the situation Tottenham were in at the start of the season, bringing so many new players in.
"To get the team playing together as a team and understanding each other in such a short period of time is nearly impossible. The fruition of the change around at Tottenham starts more next season.
"You would have to be a miracle worker to get everyone functioning to the best of their ability when they have just arrived from a foreign country into a different culture that they have never played in before."
Tim Sherwood has been placed in interim charge at White Hart Lane, with former manager Glenn Hoddle, ex-England boss Fabio Capello and Southampton's Mauricio Pochettino emerging as contenders for the full-time job.
Hoddle, who was in charge of Spurs between 2001 and 2003, is ready to return to football management with Tottenham if approached by the club.
The former England boss Hoddle has not been in club management since Wolves in 2006.
A story on a website co-founded by Hoddle suggested he is awaiting a call from White Hart Lane and read "Zapsportz.com understands that Hoddle will certainly help if the club makes an approach."
Former Tottenham owner Sir Alan Sugar, ex-Spurs striker Gary Lineker and Hoddle's former Spurs team-mate Ossie Ardiles are all backing Hoddle's appointment.
"For me, the man for the job is Glenn Hoddle," Ardiles, Spurs boss from 1993 to 1994, told TalkSPORT.
"I think he is a wonderful manager and he is a lot more mature, so I think he will be a wonderful choice.
"He knows everything about the Premier League and Spurs especially."
Villas-Boas was sacked after Sunday's 5-0 loss at home to Liverpool, with Sherwood placed in temporary charge.
Despite the Reds reverse and the earlier 6-0 defeat at Manchester City, Ardiles has confidence in the Spurs squad.
The former Argentina midfielder added: "I believe whoever is the manager will have a wonderful, wonderful squad. They have one of the best squads in the Premier League in fact.
"Unfortunately, things have not gone right this season, but in terms of the quality of our players it is absolutely second to none.
"It is a wonderful job at the end of the day. It is a big squad and a superb squad."