In a statement to lawmakers in Edinburgh, Michael Matheson blamed his teenage sons for watching football on the device while in Morocco.
He previously claimed that the eye-watering bill was a result of him working on official business during the trip in late December and early January last year.
But he backtracked after opposition parties pointed out that he would have had to send some 8,000 emails in 24 hours to incur a 7,300 pound bill on one of the days.
Matheson, who has faced increasing calls to be sacked, said he "did not knowingly run up the roaming charges bill" and had reimbursed the money in full.
"Mistakes have been made -- by me, by my family," he said. "I should have sorted the SIM card and I should have investigated what happened more thoroughly.
"I accept that, take full responsibility and apologise unreservedly," the Scottish National Party lawmaker added.
Scotland's First Minister Humza Yousaf said "honest mistakes do happen" but said he had "absolute confidence" in Matheson as a minister.
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