Despite their impressive performances, Large Language Models (LLMs) remain prone to hallucination, which critically undermines their trustworthiness. While most of the previous work focused on tackling answer and attribution correctness, a recent line of work investigated faithfulness, with a focus on leveraging internal model signals to reflect a model's actual decision-making process while generating the answer. Nevertheless, these methods induce additional latency and have shown limitations in directly aligning token generation with attribution generation. In this paper, we introduce LoDIT, a method that jointly generates and faithfully attributes answers in RAG by leveraging specific token logits during generation. It consists of two steps: (1) marking the documents with specific token identifiers and then leveraging the logits of these tokens to estimate the contribution of each document to the answer during generation, and (2) aggregating these contributions into document attributions. Experiments on a trustworthiness-focused attributed text-generation benchmark, Trust-Align, show that LoDIT significantly outperforms state-of-the-art models on several metrics. Finally, an in-depth analysis of LoDIT shows both its efficiency in terms of latency and its robustness in different settings.