The strongly pro-EU former prime minister said the country had to be “very mature and reflective” about the next steps - dismissing his successor’s call for a rapid move towards formal withdrawal.
He told Sky News: “There will be very big consequences and we need to think our way through those carefully.
“But there is no point in hiding it: for me this a very, very sad day.”
The Labour leadership was “pretty lukewarm in its support for Remain” and failed to mobilise its supporters “to understand that this was not a`protest vote against the Government or indeed the Establishment”, he added.
Mr Blair said Mr Cameron was “definitely right not to invoke Article 50 straight away”, contradicting his successor’s demand in the immediate aftermath of the vote.
He said he expected financial market turmoil would continue and said the next steps had to be taken “with a sense of unity across the political spectrum”.
In a direct blast at the Labour campaign, he said the “enormous consequences” had not been properly set out to its core support - who voted for Leave in significant numbers.
Mr Blair said that Leave campaigners had dismissed warnings of the danger of Brexit as “scaremongering”.
“I think you can see from the reactions already, those threats are real,” he said, warning that “the reality of the choice we’ve made is going to sink into the public consciousness in a big way in the days and weeks to come”.
Mr Blair said he hoped that Leave leaders like Boris Johnson and Michael Gove would “reflect on the real interests of our country” as they saw the impact of the Brexit vote unfold.
Asked if Mr Corbyn should quit, Mr Blair said: “I think there are much, much bigger questions for the Labour Party right now.
“We’ve got to consider what our purpose is, where we are going and what we are trying to do here.”
He said in the US and Europe, “the centre left and centre right have lost political traction” while “the populist insurgent movements of left and right are taking control”.
Mr Blair said: “The answers to the challenges of globalisation do not lie in shutting ourselves off from the world. And I think what we will learn in these days, weeks and months ahead, I’m afraid, is that you can ride the anger through these populist movements but you don’t actually produce the answers to the challenges people face...
“We will find that what people thought was going to be an answer to these problems is not an answer at all.”
Labour needs to “get its act together” and find “the answers to the problems people face”, he said.
Defending his decision to admit workers from new EU member states in 2004, Mr Blair said: “Although I understand the pressures that people from eastern Europe coming in living and working in this country have (created), I actually believe on the whole those people pay far more in taxes than they receive in benefits and they are good people, they are decent people and they have contributed to our country.”
It would be important to send a signal to these people - particularly those working in the NHS - that they are “still welcome here”, he said.