Mr MacAskill wants more power to allow Scottish police to pull drivers over, to set a different alcohol limit for young drivers and introduce new penalties.
However, UK Transport Secretary Patrick McLoughlin has written to him to reject his request for more devolution of powers from Westminster.
Mr MacAskill said: "The statistics on drink-driving are stark. It is estimated that on average each year there are 30 lives lost on Scotland's roads as a result of drink-driving.
"Too many people still think it is acceptable to get behind the wheel after drinking alcohol.
"The UK Government has missed an opportunity to extend the limited transfer of drink-drive powers.
"Additional powers to set penalties, to allow police to carry out breath testing at any time and to consider differential drink-driving limits – for example for young and novice drivers – could have saved lives.
"The Secretary of State for Transport has rejected our call to devolve these responsibilities but I will continue to urge the UK Government to reconsider."
A consultation seeking views on lowering the existing blood/alcohol limit of 80mg/100ml to 50mg/100ml closed last week, and the responses are being independently analysed.