(1) Background: Early signs of sepsis in a neonate are often subtle and non-specific, the clinical course rapid and fulminant. The aim of our research was to analyse diagnostic markers for neonatal sepsis and build an application which could calculate its probability. (2) Methods: A retrospective clinical study was conducted on 497 neonates treated at the Clinical Department of Neonatology of the University Children's Hospital in Ljubljana from 2007 to 2021. The neonates with a diagnosis of sepsis were separated based on their blood cultures, clinical and laboratory markers. The influence of perinatal factors was also observed. We trained several machine-learning models for prognosticating neonatal sepsis and used the best-performing model in our application. (3) Results: Thirteen features showed highest diagnostic importance: serum concentrations of C-reactive protein and procalcitonin, age of onset, immature neutrophil and lymphocyte percentages, leukocyte and thrombocyte counts, birth weight, gestational age, 5-min Apgar score, gender, toxic changes in neutrophils, and childbirth delivery. The created online application predicts the probability of sepsis by combining the data values of these features. (4) Conclusions: Our application combines thirteen most significant features for neonatal sepsis development and predicts the probability of sepsis in a neonate.