Modern recommendation systems are mostly based on implicit feedback data which can be quite noisy due to false positives (FPs) caused by many reasons, such as misclicks or quick curiosity. Numerous recommendation algorithms based on collaborative filtering have leveraged post-click user behavior (e.g., skip) to identify false positives. They effectively involved these false positives in the model supervision as negative-like signals. Yet, false positives had not been considered in existing session-based recommendation systems (SBRs) although they provide just as deleterious effects. To resolve false positives in SBRs, we first introduce FP-Metric model which reformulates the objective of the session-based recommendation with FP constraints into metric learning regularization. In addition, we propose FP-AdaMetric that enhances the metric-learning regularization terms with an adaptive module that elaborately calculates the impact of FPs inside sequential patterns. We verify that FP-AdaMetric improves several session-based recommendation models' performances in terms of Hit Rate (HR), MRR, and NDCG on datasets from different domains including music, movie, and game. Furthermore, we show that the adaptive module plays a much more crucial role in FP-AdaMetric model than in other baselines.