"The Europe of yesterday is gone, we have a Europe of today which has no principles at all," the 90-year-old told a crowd of thousands gathered in a Harare stadium to mark 34 years since the country's independence from Britain.
Mugabe, who has been Zimbabwe's ruler since independence, faces EU sanctions as a result of his authoritarian rule. He refused to attend an EU-Africa summit earlier this month after his wife was denied a visa to enter Europe.
"The Europeans will never ever accept a ZANU-PF government in this country," referring to the political party he dominates.
"What is natural is made unnatural. And what is unnatural they want to say it is natural," he said in the speech, which lasted an hour and a half.
Mugabe repeated his claims that Europe is trying to force gay rights on Africa.
"(Europe says) If you pass a law that rejects homosexual marriages we will punish you like they are doing to Uganda and us," he said.
"Let Europe keep their homosexual nonsense there and not cross over with it here."
Mugabe, who once said gays and lesbians are worse than pigs and dogs, warned Western diplomats in Zimbabwe against preaching gay rights, saying they would be deported.
His election victory last year was rejected by many Western countries amid claims of widespread rigging and intimidation.
But a defiant Mugabe has refused to brook any dissent, and threatened the main opposition Movement for Democratic Change, saying its plan to lead protests over the deteriorating economy and high unemployment would not be accepted.
"We shall never tolerate acts of violence," he said.