Villas-Boas became the seventh Spurs manager to be sacked by Levy during his reign at White Hart Lane after Sunday's 5-0 thrashing by Liverpool.
Tim Sherwood has been installed as interim boss and will remain in charge for Sunday's trip to Southampton, but a supporters' group have reacted angrily to Villas-Boas' exit and urged Levy to give reasons for his departure.
A statement read: "Following the departure of Andre Villas-Boas on Monday morning and defeat in the Capital One Cup on Wednesday evening, the board of Tottenham Hotspur Supporters' Trust believe it is paramount that the chairman of Tottenham Hotspur Football Club, Daniel Levy, issues a statement addressing the supporters to explain the rationale behind the manager's dismissal and clearly stating his plans moving forward.
"We believe that now, more than at any time during ENIC's ownership of THFC, the level of frustration and anger being shown by fans renders this request fully warranted. As ever, it is made in the best interests of our club."
Levy, who was at the club's training ground on Thursday, is considering candidates to replace Villas-Boas.
The agent of Frank de Boer has claimed Tottenham have expressed an interest in the Ajax head coach, while fellow Dutchmen Guus Hiddink and Ronald Koeman have also been linked with the job.
Sherwood has refused to rule himself out of the running but admitted the role would have to be right for him and the club.
"I need to chat to the chairman and see what they're thinking but the immediate future is up in the air," he said.
Southampton host Spurs in the Premier League on Sunday but Saints' Argentinian manager Mauricio Pochettino - widely touted as a potential replacement for Villas-Boas - says no-one from Tottenham has been in touch and that he is happy at St Mary's, especially with the backing of chairman Nicola Cortese.
"As a manager what's really important is that the sporting aspect is under my control, in terms of signings," Pochettino said.
"Without my agreement no signings go through, and those two basic things are very important for any manager."
Tim Sherwood's news conference will be shown on Sky Sports News from 1.30pm.