Pillai said the evidence against the ISI emerged from the interrogation by Indian officials of David Headley, a US citizen, who pleaded guilty to working with Lashkar to plan the attacks.
The accusation comes on the eve of talks aimed at reviving a peace process between the two countries, which was broken off after the deadly assault.
Prerna Suri, Al Jazeera's India correspondent, said that while it was not a new allegation, the timing of the statement was very significant.
"In his confessional statement, Headley named the ISI as being behind the co-ordination and logistical support of the Mumbai attacks," Suri said.
"New Delhi is sending a clear message to Pakistan that security will be the main concern during these talks.
"They [India] would like Pakistan to crack down on those groups, who they feel are operating against Indian interests, meaning LeT as well as individuals such as [its chief] Hafiz Muhammed Saeed, who many in India feel are being given patronage by various elements in Pakistan."
S M Krishna, India's foreign minister, said he would press Pakistan on the progress of its probe into the Mumbai attacks as he arrived in Islamabad on Wednesday for the meeting, saying he was looking forward to receiving feedback from the Pakistanis on India's "core concern of terrorism".
He said the issue was discussed during last month's visit of P Chidambaram, India's home minister, to Pakistan and he would raise it again in talks with Shah Mehmood Qureshi, Pakistan's foreign minister, on Thursday.
"We hope to discuss all issues of mutual interest and concerns that can contribute to restoring trust and building confidence in our bilateral relationship," Krishna said as he arrived in Islamabad.
"This is an important visit as it marks the new beginning of a journey in our effort to build a peaceful, friendly and co-operative relationship between our two countries."
Resuming dialogue between the countries is crucial not only for improving their ties but also the security outlook in Afghanistan where the two countries vie for influence.
India broke off a four-year-old peace process with Pakistan after the Mumbai attacks, saying reviving the dialogue would depend on action against Lashkar and Saeed, who India says masterminded the assault.
Pakistan has put seven people on trial for the Mumbai attacks but has maintained that India has not provided enough evidence to prosecute Saeed.
Pillai said Saaed's role in the Mumbai attacks was not "peripheral", but that "he knew everything".