Video report by ITV News Correspondent Rebecca Barry
Speaking outside his home, he told ITV News that he was "very sad" to be kicked out by the party.
He said: "I'm still in the Labour Party, as far as I'm concerned, and I'll always be Labour.
"This is the single biggest issue facing the country, Brexit, and the Labour party was hammered in these elections because of the incoherent position that was taken."
Mr Campbell declined to say who he would vote for in a snap general election were one to be held.
He said: "I want to vote Labour at the general election but that will depend on the policy that the Labour Party puts forward between now and then in relation to Brexit."
Mr Campbell said his quick expulsion was "strange" and contrasted it to the party's handling of allegations of anti-Semitism.
"I think people will inevitably draw the contrast with the lack of rapidity in dealing with cases involving anti-Semitism," he said.
He revealed the news on Twitter earlier on Tuesday, saying: "Sad and disappointed to receive email expelling me from @uklabour - particularly on , not least thanks to tactical voting by party members, including MPs, councillors and peers who back @peoplesvote--uk."
Mr Campbell added: "I am and always will be Labour.
"I voted Lib Dem, without advance publicity, to try to persuade Labour to do right thing for country/party."
He's made no secret of his support for a second, so-called People's Vote, and of his criticism of how Jeremy Corbyn has been running the party.
A Labour Party spokesman said "support for another political party or candidate is incompatible with Party membership".
The party's stance was repeated by Dawn Butler, the MP for Brent Central.
She told reporters that Mr Campbell had clearly been in violation of Labour's rule book and that it was party policy to kick members who vote for other parties out of the party.
The Labour Party suffered a humbling day at the polls, seeing the number of MEPs halved to just 10 and being beaten into fifth place in Scotland.
A number of senior figures - including deputy leader Tom Watson and shadow Brexit Secretary Sir Keir Starmer - said Labour had suffered by trying to appeal to both Remain and Leave voters while the Brexit Party, led by Nigel Farage, and the Lib Dems offered clear messages over Europe.
In contrast, Mr Campbell has been at the forefront of the campaign to stop Brexit. He declined to say who he would vote for in a snap general election were one to be held.
Instead he responded: "I want to vote Labour at the general election but that will depend on the policy that the Labour Party puts forward between now and then in relation to Brexit."
Mr Campbell claimed people in "senior positions" in Jeremy Corbyn's office had recommended voting against the Labour Party.
He added: "Jeremy Corbyn himself, for reasons best known to himself, has in the past congratulated George Galloway on defeating a Labour candidate."
Mr Campbell said former prime minister Tony Blair had refused suggestions he should withdraw the Labour whip from Jeremy Corbyn for rebelling against the party when in government.
Reaction to Campbell getting the boot from Labour
His tweets drew immediate responses from many pointing out how he would be aware of the risks of voting for another party - and also how he is still linked to the so-called 'sexed up' dossier that formed part of the case for the ill-fated Iraq War.
Indeed the grassroots Momentum network of Corbyn supporters tweeted being expelled from Labour was "the least he deserves" for his role over Iraq.
Tony Blair said he understood why his ex-aide had voted Lib Dem.
Mr Blair said he had voted Labour "without any great enthusiasm" at last week's European election.
Former Labour home secretary Charles Clarke has called on Labour to reinstate Alastair Campbell and admitted he also voted Liberal Democrat in the European elections as a "one-off".
Vauxhall MP Kate Hoey, who served in Tony Blair's Cabinet as Minister for Sport, also has responded to criticism that she should also have been expelled from the Labour Party, along with Alastair Campbell, after being accused of showing support for the Brexit Party by sharing a stage with Nigel Farage.