Alexander said the prime minister was wrong to make Europe a priority when the government was failing to manage the economy well, and accused him of putting his party's fears about the rise of Ukip ahead of the national interest.
"David Cameron's speech [will] increase instability at a time when the economy needs stability and at a time when we need growth and investment in the economy. It was the wrong speech to make," Alexander told the BBC on Saturday.
Figures released on Friday showed the economy shrank by 0.3% in the last quarter of 2012, leading to the pound falling to its lowest value against the euro since 2011.
In a speech on Wednesday, Cameron said the Conservative party would fight the next election on a platform of an "in-out" referendum on Britain's membership of the EU. The referendum would be preceded by efforts by the government to renegotiate aspects of Britain's relationship with the union.
During prime minister's questions at the House of Commons on Wednesday after Cameron's speech, the Labour leader, Ed Milliband, said that he was against an "in-out" referendum, but Alexander said the party was not against a referendum in all circumstances.
He said Labour was in favour of a referendum if significant powers were transferred from Westminster to Brussels but not in calling one before any change had taken place.
"We are clear that change is coming to the Europe. The timescale in which that change will happen and its impact on the UK all remain unclear," he said. "We think that you cannot sensibly make a judgement on that today.
"The priority has to be economic stability, and in Europe negotiating to build influence rather than lose influence."
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