This paper presents a relatively simple method that does not require the use of any special software and allows one to assess objects with the help of a matrix of quantified indicators. This method has been applied to assess innovative activities in federal subjects in the period 2005–2009. A study of the innovative activity in federal subjects has shown that the level of innovative activity of economic agents in Russia changed in the period 2005–2009. These changes were largely due to the creation of novelties and demand for innovation, which could be particularly observed during the critical phase of the financial and economic crisis in the period 2007–2008. The impact of demand for innovations has been insignificantly higher than that of their supply. The excess of demand over supply has stimulated the development of new products and technologies. However, with the alleviation of crisis consequenses in the Russian economy, the importance of demand for innovations has shrunk, whereas the role of the economic capacity of economic entities to deploy innovations has grown. In the period of 2005–2006, the number of innovatively active regions in Russia was insignificant. The innovation activities have occurred in different areas and in various ways. A gap between the level of innovative activity of the innovatively active and innovatively passive regions in Russia has increased. Based on the results of the study, one can argue that in the midterm outlook, the innovative development in Russia can only be evolutionary rather than revolutionary or of a breakthrough nature.