People use digital media and the Internet daily. The time that young people spend connected to digital devices will increase as technology advances, which could have severe health risks and behavioral dependence implications. In the context of the current pandemic, in which socializing, studying, and working is changing, this question has become particularly relevant. Therefore, we propose to investigate the perceptions of young university adults—understood as generation Z—regarding their digital media practices, particularly during the pandemic, and to study the consequences of a permanent connection to these formats on the development of an addiction to the Internet. Our quantitative method approach applied questionnaires to a sample of 407 young university adults studying in Portugal. Through this survey, we could target a specific user group, quantify their consumption, and measure their online experiences. The results point to an increase in dependence on the Internet during confinement. While it is true that carrying out academic work is one of the reasons for this growth, it is noteworthy that the respondents sought the online world in a significan way to pass the time and escape their routine. In addition, they confess to experiencing some consequences of excessive use, such as sleep disturbances and adverse emotional reactions—such as instabilities, depression, and nervousness—when not online. We conclude that the pandemic has intensified online dependence. However, above all that, it is necessary to look at the mental and general health consequences that this excessive use has brought, which may not be visible or manifested by the youth in the short term, and may come to have consequences in the long term.