Three gay rights groups -- Zagreb Pride, LORI and Rainbow Families -- and the RODA parents' rights group issued a statement labelling the book burning a "public incitement to violence and hatred".
A criminal complaint has been filed with prosecutors, the statement added.
Kastela's mayor defended the organisers, saying that the carnival has an annual tradition of burning something that symbolises evil.
"The town has never interfered into the carnival association's decisions" mayor Denis Ivanovic told local media."
The rights groups dismissed this excuse.
"Although the burning was done within the carnival context it does not remove the organisers' responsibility since... it calls to hatred towards a minority," the groups said.
The book burning was also condemned by the country's education minister and ombudsman for children.
It took place barely two weeks after the book's official launch by Rainbow Families, an association of lesbian, gay and transgender people who have or plan to have children.
The group published 500 copies of the book available free of charge.
Nearly 90 percent of Croatians are Roman Catholic, and a Church-backed group earlier in January criticised the book, which it described as "controversial".
Croatia, the European Union's newest member state since 2013, has seen a gradual liberalisation of gay rights in recent years.
Homosexual couples have been able to register as "life partners" since 2014, with many of the same rights as heterosexual married couple.
But the law does not include provisions regulating the adoption of children, leaving it down to state-run bodies to decide on individual applications.