Preterm birth is associated with life-long cost implications on the infant, family, health system, and society at large. The costs related to lost productivity at contributions at work during care of preterm infants are difficult to measure. We aimed to explore and document the unpriced costs parents incur following birth of a preterm infant in the first year of life in a low resource setting. Thirty-nine mothers and five fathers of preterm infants who had ever attended the preterm follow-up clinic after discharge from Mulago National Referral Hospital, were included in a qualitative study between November 2019 and February 2020. Participants were purposively selected, and data were collected using four focused group discussions with mothers and in-depth interviews with the fathers lasting 30-70 minutes each. These were audio-recorded, transcribed and translated. The data were manually analysed using the thematic approach. Three themes were generated: i) complex nature of the infant, ii) time to care for the infant, iii) mother as the predominant caregiver. The parents perceived preterm infants as delicate, complicated and their care more costly compared to those born at term. Expressions of need for time to care for their infants, frequent hospital visits and readmission were raised. Availability of the mother as the predominant caregiver some of whose roles cannot be delegated and their experiences following return to work after birth of a preterm were cited by the participants. The results highlight the unpriced costs incurred by the parents through disruption of the work pattern due to the actual and perceived needs of a preterm infant and time to care in a low resource setting. We recommend guidance on financial planning, development of policies and programs on social and financial support for parents and future studies on indirect costs of preterm care.