The law had cost convenience stores more than £16m, the Scottish Grocers' Federation said, while Spar wholesaler CJ Lang claimed Spar stores alone had spent between £3m and £4m.
Retailers have had to apply for new licences, train staff, change opening hours and create a separate area of the store for alcohol.
Botterills Convenience Stores said it had spent £125,000 bringing its 52 licensed premises in line. "It's been an administrative nightmare. We have probably spent £125,000 in legal costs and it's been virtually a full-time job for me for the past few months," said MD Lizette Craig.
Retailers are also angry the Scottish government has given no firm guidance on the rules for promotions, instead leaving it up to local licensing authorities to decide which promotions should be banned.
They are calling on the Scottish government, which is drawing up an Alcohol Bill by the end of the year that will cover all aspects of its consumption in Scotland, to consider the cost to businesses before making any proposals.
"For retailers, the compliance costs and burdens of the Licensing Act have been out of proportion," said Scottish Retail Consortium director Ian Shearer. "It again calls into question the rush to yet more legislation later this year."