The interpretation of implicit meanings is an integral aspect of human communication. However, this framework may not transfer to interactions with Large Language Models (LLMs). To investigate this, we introduce the task of Implicit Information Extraction (IIE) and propose an LLM-based IIE pipeline that builds a structured knowledge graph from a context sentence by extracting relational triplets, validating implicit inferences, and analyzing temporal relations. We evaluate two LLMs against crowdsourced human judgments on two datasets. We find that humans agree with most model triplets yet consistently propose many additions, indicating limited coverage in current LLM-based IIE. Moreover, in our experiments, models appear to be more conservative about implicit inferences than humans in socially rich contexts, whereas humans become more conservative in shorter, fact-oriented contexts. Our code is available at https://github.com/Antonio-Dee/IIE_from_LLM.