Background and Objectives: Anticoagulants are a well-known risk factor for gastrointestinal bleeding (GIB). In recent years, direct oral anticoagulants (DOACs) have taken a leading role in the treatment and prevention of thromboembolic incidents. The aim of this study was to investigate the prevalence of DOAC-treated patients with GIB whose plasma drug concentrations exceeded the cut-off values reported in the literature and to evaluate their clinical characteristics. Materials and Methods: Patients who were admitted to the Intensive Care Unit in the period 2/2020–3/2022 due to GIB were prospectively included in the study and classified into three groups according to the prescribed type of DOAC (apixaban, rivaroxaban, and dabigatran). For all participants, it was determined if the measured plasma drug levels exceeded the maximum serum concentration (Cmax) or trough serum concentration (Ctrough) obtained from the available data. A comparison of clinical parameters between the patients with and without excess drug values was performed. Results: There were 90 patients (54.4% men) included in the study, of whom 27 were treated with dabigatran, 24 with apixaban, and 39 with rivaroxaban. According to Cmax, there were 34 (37.8%), and according to Ctrough, there were 28 (31.1%) patients with excess plasma drug values. A statistically significant difference regarding excess plasma drug values was demonstrated between DOACs according to both Cmax (p = 0.048) and Ctrough (p < 0.001), with the highest rate in the group treated with dabigatran (55.6% for Cmax and 59.3% for Ctrough). Multivariate logistic regression showed that age (OR 1.177, p = 0.049) is a significant positive and glomerular filtration rate (OR 0.909, p = 0.016) is a negative predictive factor for excess plasma drug values. A total of six (6.7%) patients had fatal outcomes. Conclusions: Plasma drug concentrations exceed cut-off values reported in the literature in more than one-third of patients with GIB taking DOAC, with the highest rate in the dabigatran group. Clinicians should be more judicious when prescribing dabigatran to the elderly and patients with renal failure. In these patients, dose adjustment, plasma drug monitoring, or substitution with other, more appropriate DOACs should be considered.