May told The Sun newspaper that if Britain were still negotiating with the bloc in the run-up to a national election, "the Europeans might have seen that as a time of weakness when they could push us".
She passed the required minimum needed of 434 MPs in support, after opposition MPs, mainly from Labour and the Liberal Democrats, voted in favor of an election.
"That would be in nobody's interest", May said.
Labour leader Jeremy Corbyn faced down calls from some MPs at a Westminster meeting on Tuesday evening for the party to abstain in the hope of forcing Mrs May to call a vote of no confidence in her own government. She obviously thinks she can get away with it: even if swing voters have doubts about her, they are not about to bolt to the deeply unpopular hard-left Labour leader, Jeremy Corbyn.
Despite Corbyn's bravado, his party is demoralized and divided under his left-wing leadership and is expected to fare badly.
He dismissed the PM's argument that she needs a fresh mandate to deliver Brexit, and said it was "extremely interesting" she had called for an election as the Crown Prosecution Service decides whether to press charges against a number of Tory MPs over allegations relating to 2015 election expenses.
Currently, the Conservative Party has a narrow majority of 330 of the 650 seats in the House of Commons.
Tim Farron, the leader of the Liberal Democrats, asked: "What is she scared of?" The Lib Dems' credibility as the party of opposition can only be strengthened by the potential return of former heavyweights Vince Cable, Ed Davey and Simon Hughes.
"It's the right decision, it's in the national interest, and that's what this election is about".
Both Sturgeon's Scottish Nationalists and the Liberal Democrats want Britain to remain in the EU's single market - something May has ruled out, along with a referendum on any deal she wins.
But Labour MP Gisela Stuart, one of the architects of Brexit as co-chair of Vote Leave, said she would be standing down after 20 years as MP for Birmingham Edgbaston.
"This election is about her Government's failure to rebuild the economy and living standards for the majority".
May made a unexpected announcement Tuesday that she would seek a "snap" election less than halfway through her government's five-year term, with the aim of gaining a stronger mandate for the country's historic withdrawal from the European Union.
Leaders of European Union states are due to adopt negotiating guidelines at an April 29 summit, and the bloc will prepare detailed plans for the talks with Britain by late May.
The gap before talks begin in earnest in June gave her a "window of opportunity" to strengthen her hand by improving her slim 17-seat majority and pushing the next election date back to 2022, by which time the United Kingdom should have long ago left the EU.
But the Prime Minister has refused to take part in televised leaders' debates.
As the Commons backed the General Election - which will be held just over two years after the Conservatives won a narrow victory in the May 2015 poll - senior politicians from all parties have been clarifying their intentions. "We need a general election and we need one now", she said.
"The prime minister's attempt to dodge scrutiny shows how she holds the public in contempt", he said.
Her decision came on a day when ITV became the first broadcaster to confirm a debate ahead of the poll in June, announced by May yesterday.