The freshness of Atlantic salmon is influenced mainly by tissue metabolism, which in turn is affected by storage time and conditions. The alterations in taste profiles and nutritional values of salmon when packaged using vacuum methods have not been fully understood, and the factors contributing to these changes require further research. In this work, the extraction method for flavor nutrients from salmon was optimized via the Plackett–Burman (PB) test. A sensitive and rapid targeted metabolomics method for the simultaneous determination of 34 nutrients was successfully established via ultra-performance liquid chromatography–triple quadrupole/linear ion trap composite mass spectrometry (UHPLC-QTRAP/MS), and various nutritional compositions during storage at 0 °C under different vacuum conditions (0 kPa or −90 kPa) for 4 and 8 days were analyzed. Results showed that storage time had a significant effect on salmon metabolism. The total amino acids decreased by 62.95% and 65.89% at 0 kPa and −90 kPa, respectively. Notably, a marked reduction in histidine after 8 days at −90 kPa may have diminished bitterness, while decreased levels of umami-tasting amino acids like glutamine and aspartic acid affected the overall flavor profile. Overall, the packaging conditions at 0 °C and 0 kPa were more suitable for the preservation of most nutrients in salmon. Pathway enrichment analysis revealed that the reduction in substances was mainly related to the alanine, aspartate, and glutamate metabolism pathways. Alanine, inosine, and histidine, whose levels changed significantly, can bind to the typical umami taste receptor TIR1/TIR3 and can be biomarkers to monitor and determine the freshness or spoilage of salmon after 4–8 days of storage. This study revealed the changes in small-molecule nutrients in salmon during storage under different packaging conditions, which provides a reference for the packaging preservation technology of fresh salmon and new ideas for the evaluation of salmon quality and determination of freshness.