Prospective registration of study protocols in clinical trial registries is a useful way to minimize the risk of publication bias in meta-analysis, and several clinical trial registries are available nowadays. However, they are mainly used as a tool for searching studies and information submitted to the registries has not been utilized as efficiently as it could. In addressing publication bias in meta-analyses, sensitivity analysis with the Copas selection model is a more objective alternative to widely-used graphical methods such as the funnel-plot and the trim-and-fill method. Despite its ability to quantify the potential impact of publication bias, the Copas selection model relies on sensitivity analyses, in which some parameters are varied across a certain range. This may result in some difficulty in interpreting the results. In this paper, we propose an alternative inference procedure for the Copas selection model by utilizing information from clinical trial registries. Our method provides a simple and accurate way to estimate all unknown parameters of the Copas selection model. A simulation study revealed that our proposed method resulted in smaller biases and more accurate confidence intervals than existing methods. Furthermore, three published meta-analyses were re-analyzed to demonstrate how to implement the proposed method in practice.