Carbon emission is one of the most important topics in the environmental and economic issues. Although previous studies have largely revealed the drivers of carbon emissions, there is still a big challenge to uncover the impacts of the positions of countries in the global supply chains. This paper combined multi-regional input-output analysis, complex network and panel regression analysis to quantify the influence of the roles of countries in the global carbon emissions embodied in trade (EET) transfer networks on their direct carbon emissions. The results showed the network structures had significant evolutionary characteristics. Countries played different roles in the embodied carbon emission transfers, and their roles changed over time. Furthermore, we found the direct carbon emissions of countries were significantly determined by some roles in the networks, including import universality, import strength, media capability and the importance of transfer partners. Our work demonstrated the import of embodied carbon emissions significantly decreased countries' direct carbon emissions. For the global emission reduction, these important importing countries should reduce their domestic consumptions, and take the responsibility to help their import sources reduce the environmental pressure. It also indicated developing the trade relations with some important countries would help reduce the unnecessary carbon emissions in the domestic productions. Moreover, our work indicated reducing carbon emissions should consider both direct and indirect influence from the entire supply chains. One country's carbon emission reduction would need the improvement of the trade structures of all the direct and indirect importer and exporters in the same supply chain.