Increasing the efficiency of enterprises active in innovations is one of the most important factors in the development of the country's economy. However, based on analysis of the state statistics data, it can be concluded that Russian enterprises are insufficiently ready for innovation. We have analyzed the reasons for low innovative activity in Russia and suggested the methods that would increase innovative activity of enterprises. To achieve our goals, we have studied the concept of innovation process and the theory of constraints in innovation process. We have carried out comprehensive analysis of the factors and constraints affecting innovative activity of companies. It is shown that the main factors that negatively affect the innovation activity of enterprises are economic factors, such as lack of finance, high cost of innovation, economic risk during project implementation, as well as inability to determine the economic benefit from the project. Resource, effective and market constraints in innovation process are considered. It is revealed that resource, in particular financial, constraints play the greatest role in innovation activity of enterprises. In this regard, the main sources of financing innovation have been analyzed. It is shown that the main sources of financing in modern conditions are borrowed funds in the financial and credit market, as well as self-financing of the enterprise at the expense of the company's profits and additional issue of shares. We have considered the ways to overcome financial constraints when using different types of financing. The scientific novelty of our study is in determining the connection between financial position of the company and its ability to finance innovation, which is especially important in the context of financial constraints. Based on the identified connections, we have determined the indicators for assessing the financial and economic performance of an enterprise that characterize its ability to innovate. It is shown that taking into account such indicators as solvency and financial stability will allow the company to provide a high degree of investment attractiveness to increase the ability to attract borrowed funds, and maintaining a high level of indicators such as profitability and business activity will improve the efficiency of financing innovation activities from the company's own funds. The main result of the study is the developed system of key performance indicators which have an impact on increasing the innovative activity of companies in the context of financial deficit. Timely recording and maintaining the required level of these indicators will lead to an increase in the efficiency of innovation and investment activities of the enterprise; this conclusion makes this work relevant.