Estimating power consumption in modern Cloud is important to account for the power consumed by each container. The challenge is that multiple customers are sharing the same hardware platform, where physical information is mostly obscured. In addition, there is the overhead in power consumption that the Cloud control plane induces. This paper addresses these challenges and introduces a pipeline framework for container power model training on the basis of available performance counters and other metrics. The proposed model utilizes machine learning techniques to predict the power consumed by the control plane and associated processes, and uses it for isolating the power consumed by the user containers, from the server power consumption. Applying the proposed power model does not require online power measurements, nor does it need machine information, or information on other tenants sharing the same machine. The results of cross-workload, cross-platform experiments demonstrated the higher accuracy of the model when predicting power consumption of unseen containers on unknown platforms, including on virtual machines.