Background: In the rooming-in system, mothers and their healthy newborns stay together for 24 h a day; however, many women in the early postpartum period often find it challenging to balance their recovery from childbirth with the demands of caring for their newborns. This study aims to investigate the need for postpartum women to entrust their newborns to medical staff for care, and the relationship of this need with perceived pain, fatigue, and anxiety. Methods: The study uses the Need to Entrust a Newborn under the Care of the Staff (NEN) scale and the Numerical Rating Scale (NRS) to assess participants’ levels of pain, fatigue and anxiety. These scales were chosen to provide a comprehensive assessment of participants’ needs and experiences. Results: The results of the study reveal that fatigue levels among study participants were significantly high, with an Me of 7.0 (IQR = 4.0), exceeding the reportable levels of both pain (Me = 6.0, IQR = 5.0) and anxiety (Me = 5.0, IQR = 6.0) The need for support during the day and at night was at a similar level and strongly correlated (rho = 0.723; p < 0.001). Pain levels showed a significant positive correlation with the need to entrust the newborn both during the day (rho = 0.296; p < 0.001) and at night (rho = 0.332; p < 0.001). During the daytime, the correlation of fatigue with the need for staff support was rho = 0.423 (p < 0.001), while overnight, this increased to rho = 0.485 (p < 0.001). Anxiety significantly correlated with the need for staff support, both during daytime (rho = 0.422; p < 0.001) and overnight (rho = 0.431; p < 0.001). Multiparas reported significantly lower results of anxiety (U(Z) = −13.224, p < 0.001). Conclusions: The need to entrust newborns to the care of maternity rooming-in staff is strong but is often unmet in many facilities. Further research should be conducted to explore solutions, and plan future actions to alleviate the burdens on postpartum women and facilitate their recovery.