Serverless computing is an emerging cloud paradigm with serverless functions at its core. While serverless environments enable software developers to focus on developing applications without the need to actively manage the underlying runtime infrastructure, they open the door to a wide variety of security threats that can be challenging to mitigate with existing methods. Existing security solutions do not apply to all serverless architectures, since they require significant modifications to the serverless infrastructure or rely on third-party services for the collection of more detailed data. In this paper, we present an extendable serverless security threat detection model that leverages cloud providers' native monitoring tools to detect anomalous behavior in serverless applications. Our model aims to detect compromised serverless functions by identifying post-exploitation abnormal behavior related to different types of attacks on serverless functions, and therefore, it is a last line of defense. Our approach is not tied to any specific serverless application, is agnostic to the type of threats, and is adaptable through model adjustments. To evaluate our model's performance, we developed a serverless cybersecurity testbed in an AWS cloud environment, which includes two different serverless applications and simulates a variety of attack scenarios that cover the main security threats faced by serverless functions. Our evaluation demonstrates our model's ability to detect all implemented attacks while maintaining a negligible false alarm rate.