Public perceptions and expectations of inflation shape household spending, wage bargaining, and policy support, making them key determinants of macroeconomic outcomes. However, current measures rely on infrequent surveys and offer limited insight into underlying narratives and sector-specific concerns. This paper presents a novel approach to measuring public perception of inflation, using lightweight large language models (LLMs) fine-tuned on domain-specific Reddit data. We created an inflation classifier trained on posts related to components of the U.S. Consumer Price Index (CPI). When applied to more than 10 years of Reddit discussions (2012-2022), this classifier produces monthly Reddit inflation scores (RIS), which we validated against actual economic indicators. Our results show that fine-tuned lightweight LLMs perform well even with smaller training datasets, and the Reddit inflation scores strongly correlate with CPI (r=0.91) and closely align with the University of Michigan: Inflation Expectation (MICH). Importantly, Granger causality tests suggested that social media-based inflation scores often precede movements in both CPI and MICH, indicating their potential as predictive, forward-looking economic signals. Furthermore, change-point and lexical analyses uncovered shifts in inflation-related narratives across sectors like groceries, transportation, and housing, revealing dimensions of inflation concern that are not directly observable in aggregate price indices. By complementing traditional economic indicators with narrative-rich signals, this study demonstrates how NLP-based measures can facilitate earlier detection of inflationary pressures and policy responses.