Cook Inlet fore‐arc basin in south‐central Alaska is a large, deep (7.6 km) sedimentary basin with the Anchorage metropolitan region on its margins. From 2015 to 2017, a set of 28 broadband seismic stations was deployed in the region as part of the Southern Alaska Lithosphere and Mantle Observation Network (SALMON) project. The SALMON stations, which also cover the remote western portion of Cook Inlet basin and the back‐arc region, form the basis for our observational study of the seismic response of Cook Inlet basin. We quantify the influence of Cook Inlet basin on the seismic wavefield using three data sets: (1) ambient‐noise amplitudes of 18 basin stations relative to a nonbasin reference station, (2) earthquake ground‐motion metrics for 34 crustal and intraslab earthquakes, and (3) spectral ratios (SRs) between basin stations and nonbasin stations for the same earthquakes. For all analyses, we examine how quantities vary with the frequency content of the seismic signal and with the basin depth at each station. Seismic waves from earthquakes and from ambient noise are amplified within Cook Inlet basin. At low frequencies (0.1–0.5 Hz), ambient‐noise ratios and earthquake SRs are in a general agreement with power amplification of 6–14 dB, corresponding to amplitude amplification factors of 2.0–5.0. At high frequencies (0.5–4.0 Hz), the basin amplifies the earthquake wavefield by similar factors. Our results indicate stronger amplification for the deeper basin stations such as near Nikiski on the Kenai Peninsula and weaker amplification near the margins of the basin. Future work devoted to 3D wavefield simulations and treatment of source and propagation effects should improve the characterization of the frequency‐dependent response of Cook Inlet basin to recorded and scenario earthquakes in the region.