Taking due account of users’ perspectives is crucial for improving the quality of healthcare services. This study aimed to analyse the representations and evaluation criteria that users of a public health agency express towards care and treatment services and to explore whether and how the content and meaning of their communications varied according to pre-pandemic, pandemic or post-pandemic periods. A total of 501 communications sent to the public relations office of an Italian health agency were collected. An automatic content analysis procedure was applied to the textual corpus. Four main thematic cores were identified concerning the request for care and respect, the value of the doctor–patient relationship and the difficulties in contacting services and accessing care. Two main latent dimensions of meaning were identified, which capture the dialectic between the demand for relationships and the demand for access to care, and between attention to the relational competence of health workers and attention to the needs and rights of users. Communications collected during the pre-pandemic and post-pandemic periods mainly concern the difficulty of access to care; those collected during the pandemic period mainly concern the doctor–patient relationship. Interpersonal aspects and timely access to care appear to be crucial in users’ assessment of the quality of care.