Speaking to journalists on the first official day of business, Dr Rowan Williams said his message to the around 210 absent bishops was: "We're sorry you're not here."
"The great pity is that to have those voices in the discussion as we conceived it would have been a healing and a helpful thing," he said.
The boycotting bishops, largely from the Global South, are angry over the attendance at Lambeth of pro-gay clergy, including some of those involved in the 2003 consecration of the openly homosexual Gene Robinson as Bishop of New Hampshire.
They held an alternative gathering in Jerusalem last month, the Global Anglican Future Conference (GAFCON), during which they accused parts of the Anglican Communion of teaching the "false gospel" of homosexuality.
Dr Williams re-affirmed the Anglican Communion's official position on human sexuality, saying that it did not endorse sex outside of marriage and that the Anglican Communion had made its position "corporately clear" in previous Lambeth Conferences. He was referring to Resolution 1.10 agreed by bishops at the 1998 Lambeth Conference, which rejected homosexuality as incompatible with Scripture and reaffirmed marriage as a union between a man and a woman.
The Archbishop of Canterbury rejected talk of a schism in the 70 million-strong Anglican Communion.
"If this is the end of the Anglican Communion, I don't think anyone has told the rest of the people here," he quipped.
Dr Williams acknowledged concerns over the legitimacy of Lambeth's outcomes in light of the bishops' absence, but hinted that the discussion process would continue with or without them.
"It's a point I put as strongly as I can to those who are not here, that if they want their voices incorporated in this, this is the way to do it."
He said the anger of the provinces that have pulled out of Lambeth, including Nigeria, Rwanda, Kenya, Uganda and Sydney, would need to be addressed in the coming months and years ahead.
The wife of the Rt Rev Pierre Whalen, Bishop of the Convocation of Episcopal Churches in Europe, echoed the Archbishop's sentiments.
Joining him at the press conference as a spokeswoman for the parallel spouses' conference, Melinda Whalen said they missed the contribution of the wives of bishops boycotting the conference.
"We miss hearing their stories and we miss the contribution they could have made to our conference if they had joined our conference."
Dr Williams said he did not believe the recent General Synod vote reaffirming support for women bishops had caused the Church of England to enter the Lambeth Conference as a "bleeding, hunted animal with arrows in its side".
In his opening presidential address yesterday, Dr Williams outlined his vision of unity achieved by consent and not coercion.
"It's my conviction that the option to which we are being led is one whose keywords are of council and covenant. It is the vision of an Anglicanism whose diversity is limited not by centralised control but by consent," he said, elaborating on Monday that the council would take the form of an international advisory body.
"That is a vision worth working for and worth sharing with our ecumenical partners," he told journalists at the press conference.
The once-in-a-decade Lambeth Conference, currently taking place at the University of Kent in Canterbury, will see more than 600 bishops tackle issues such as human sexuality, the environment and the draft Anglican Covenant, a document that attempts bind the Anglican Communion's 38 provinces into a process of joined-up deliberation whenever disputes over contentious issues occur.
On Thursday, the bishops will march through central London to highlight the Millennium Development Goals and press world governments to do more to ensure they are reached by the target date of 2015.
