Large language models (LLMs) are increasingly integrated into high-stakes decision-making. Inspired by the theory of \emph{inattentional blindness} in human cognition, we investigate whether LLMs, trained on human-preferred corpora that embed attentional biases, exhibit a similar limitation: \emph{failing to attend to subtle yet important contextual cues under explicit task instructions}. To evaluate this, we introduce the task of \textbf{explicit-implicit reasoning} and present \textbf{MixRea}, a benchmark of 2,246 multiple-choice questions across 9 reasoning types with varying distributions of explicit and implicit information. Evaluation of 21 advanced LLMs shows that even the best-performing reasoning model (Gemini 2.5 Pro) achieves only 42.8\% consistency, revealing widespread inattentional blindness. To mitigate this, we propose \textbf{Potential Relation Completion Prompting (PRCP)}, a prompting method that improves reasoning by recovering overlooked causal relations. Further analysis shows that this limitation persists across diverse multi-source reasoning tasks, highlighting the need for more cognitively aligned models.