Calls from the former prime minister for pro-Europeans to form a new cross-party movement to persuade leave-voters they got it wrong prompted a backlash, with Foreign Secretary Boris Johnson calling him "condescending".
While warning a u-turn on Brexit could undermine future referenda and the political process, Andrew Flannagan from Christians on the Left - which campaigned for a Remain vote - said Mr Blair's voice should be heard.
He told Premier's News Hour: "I certainly fundamentally disagreed with Tony Blair on quite a few things, including the Iraq War ...but you can't not say that he's an expert.
"He does know what he's talking about in all of these international matters, having dealt with the European Union [and] having dealt with the rest of the international community for such a long time.
"To ignore what somebody who is expert in this world is saying is tantamount to ridiculous and I think that it speaks to that bigger picture of ignoring what the expects said on the run-up to the Brexit vote as well."
In a speech at the London headquarters of Bloomberg on Friday, Mr Blair said Britain's withdrawal from the EU was not inevitable and voters did not understand the consequences of Brexit - including a stronger possibility of Scottish independence.
He said: "This is not the time for retreat, indifference or despair; but the time to rise up in defence of what we believe - calmly, patiently, winning the argument by the force of argument; but without fear and with the conviction we act in the true interests of Britain."
Criticising Mr Blair's credibility, Boris Johnson said: "This is the guy who would have taken our country into the euro with what would have been catastrophic consequences.
"This is the guy who dragooned the United Kingdom into the Iraq War on a completely false prospectus with consequences which foreign ministers here are still trying to deal with.
"I urge the British people to rise up and turn off the TV next time Blair comes on with his condescending campaign."
Mr Blair's speech also came under fire from Ukip leader Nigel Farage and the Conservative MP and leave campaigner Iain Duncan Smith.
Andrew Flannagan added: "I don't we should be clamping down on those who are voicing their opposition and those are saying 'we don't think this is good, we don't think that way it is happening is good'."
Click here to listen to Andrew Flannagan speaking with Premier's Aaron James: