Relational Triple Extraction (RTE) is a fundamental task in Natural Language Processing (NLP). However, prior research has primarily focused on optimizing model performance, with limited efforts to understand the internal mechanisms driving these models. Many existing methods rely on complex preprocessing to induce specific interactions, often resulting in opaque systems that may not fully align with their theoretical foundations. To address these limitations, we propose SMARTe: a Slot-based Method for Accountable Relational Triple extraction. SMARTe introduces intrinsic interpretability through a slot attention mechanism and frames the task as a set prediction problem. Slot attention consolidates relevant information into distinct slots, ensuring all predictions can be explicitly traced to learned slot representations and the tokens contributing to each predicted relational triple. While emphasizing interpretability, SMARTe achieves performance comparable to state-of-the-art models. Evaluations on the NYT and WebNLG datasets demonstrate that adding interpretability does not compromise performance. Furthermore, we conducted qualitative assessments to showcase the explanations provided by SMARTe, using attention heatmaps that map to their respective tokens. We conclude with a discussion of our findings and propose directions for future research. Our code is available at https://github.com/Chen-XueWen/SMARTe.