The aim of this study is to investigate perceptions of parents in Croatia towards advantages and disadvantages of computer use in general as well as their children's computer use and to reveal parents' concerns and opinions about digital technology (DT) education in kindergarten. The paper reports on research findings from one of the large public kindergartens in the capital city of Croatia. A total of 152 parents of the children aged 3 to 7 enrolled at this early childhood education institution filled in the survey. Results show that although being very well equipped with digital technology hardware at home (99% of surveyed parents owns a computer, tablet or smartphone), parents feel anxious and are not always willing to allow their children to use DT. Results of our survey reveal young children's ability to use DT, but they also show that mere possession of DT at home and enabling children to use computers does not guarantee development of computer literacy and/or information literacy skills.