COVID-19 now ranks among the most devastating global pandemics in history. The causative virus, SARS-CoV-2, is a new human coronavirus (hCoV) that spreads among humans and animals. Great efforts have been made to develop therapeutic agents to treat COVID-19, and among the available viral molecular targets, the cysteine protease SARS-CoV-2 M is considered the most appealing one due to its essential role in viral replication. However, the inhibition of M activity is an interesting challenge and several small molecules and peptidomimetics have been synthesized for this purpose. In this work, the Michael acceptor cinnamic ester was employed as an electrophilic warhead for the covalent inhibition of M by endowing some peptidomimetic derivatives with such a functionality. Among the synthesized compounds, the indole-based inhibitors 17 and 18 efficiently impaired the replication of beta hCoV-OC-43 in the low micromolar range (EC = 9.14 μM and 10.1 μM, respectively). Moreover, the carbamate derivative 12 showed an antiviral activity of note (EC = 5.27 μM) against another hCoV, namely hCoV-229E, thus suggesting the potential applicability of such cinnamic pseudopeptides also against human alpha CoVs. Taken together, these results support the feasibility of considering the cinnamic framework for the development of new M inhibitors endowed with antiviral activity against human coronaviruses.