The Orkney and Shetland MP has faced calls to resign after admitting the leak of a memo during the election.
It suggested First Minister Nicola Sturgeon would prefer David Cameron as prime minister over Ed Miliband.
Mr Carmichael has denied he acted unlawfully.
The petition was lodged at the court of session in Edinburgh last month to challenge the Orkney and Shetland constituency result.
Papers lodged by Mr Carmichael's legal team said that he has "not committed any illegal practice", although he does accept "mis-stating his awareness of the leaked memorandum", which he originally claimed no knowledge of.
His lawyers said this was "an error of judgement on a political matter" and "it did not amount to a false statement of fact".
The Parliamentary Standards Commissioner has launched a formal inquiry into the conduct of Mr Carmichael. The watchdog will consider Mr Carmichael's actions under the MPs' code of conduct.
The confidential memo at the centre of the controversy was written by a civil servant in the Scotland Office.
It was a third-hand account of a conversation between Ms Sturgeon and the French ambassador, in which Ms Sturgeon was reported to have said she wanted David Cameron to remain as prime minister.
Both the first minister and the ambassador insisted this was not the case, and the memo had contained a disclaimer that parts of the conversation may have been "lost in translation".
Mr Carmichael had denied knowing about the memo when asked about the leak at the time, claiming the first he had heard of it was when he received a phone call from a journalist.
He has since apologised and accepted full responsibility for the leak. Mr Carmichael has rejected calls to resign.
A group pursuing legal action against former Scottish Secretary Alistair Carmichael has reached its £60,000 target for funding its case.