Several works of literature contributed to the web evaluation process in recent years to promote digital inclusion by addressing several accessibility guidelines, methods, processes, and techniques. Researchers have investigated how the web evaluation process could be facilitated by including accessibility issues to obtain an inclusive and accessible solution to improve the user experience and increase user satisfaction. Three systematic literature reviews (SLRs) have been conducted in the context of past research, considering such research focuses. This paper presents a new SLR approach concerning accessibility in the web evaluation process, considering the period from 2010 to 2021. The review of 92 primary studies showed the contribution of publications on different phases of the web evaluation process mainly by highlighting the significant studies in the framework design and testing process. To the best of our knowledge, this is the first study focused on the web accessibility literature reporting the engineering assets for evaluation of new accessible and inclusive web-based solutions (e.g., websites). Besides, in this study, we aim to provide a new direction to the web designers and developers with an updated view of process, methods, techniques, tools, and other crucial aspects to contribute to the accessible process enrichment, as well as depict the gaps and challenges that may be worthy to be investigated in the future. The findings of this SLR introduce a new dimension in web accessibility research on determining and mitigating the research gap of web accessibility issues for web designers, developers, and other practitioners.