Parliamentary Secretary Mario Galea offered to step down from Parliament after Thursday's mistake when he voted with the opposition but the Prime Minister and the Nationalist parliamentary group did not accept his resignation.
Mr Galea said yesterday he was "broken" and "very down" after the mistake, which saw him vote in favour of a Labour motion that condemned the government on the Delimara power station extension contract.
"I apologised to the parliamentary group for being an embarrassment and offered to resign if they felt it was the best thing to do," Mr Galea said, adding he wanted to shoulder responsibility for his mistake.
However, his offer was "solidly" turned down by the parliamentary group and the Prime Minister, who, according to Mr Galea, accompanied him out of Parliament.
Mr Galea regretted the fact that his mistake was being "exploited" by the Labour Party.
"When the roll call started I was engaged in a cross debate with opposition whip Joe Mizzi over the interpretation of Parliament's standing orders and when I heard my name I said yes.
"It was a genuine mistake, which I tried to correct immediately," he explained, insisting he had never criticised the power station extension project and was always loyal to the PN and Lawrence Gonzi.
When asked about Foreign Minister Tonio Borg's claim that Labour MP Justyne Caruana voted with the government against the motion, Mr Galea said he did not hear her vote because, at the time, he was distracted.
"The way Parliament votes is very chaotic. It is very easy for anybody to get distracted and make a mistake.
"The Clerk of the House calls out the names in alphabetical order and, in the middle of cross debates, all you hear is yes or no," Mr Galea said, calling for changes to the system because it was prone to confuse MPs and lead to mistakes.
"Voting is not a quiz and MPs should be allowed to change their preference if there is a genuine mistake," he said.