How were the europeans able to dominate so many larger countries?

Although they were smaller, generally speaking, they had access to better technologies. For example, the industrial revolution began in Great Britain. This gave them access to state of the art materials for the time, that they could use in both diplomacy and war. Apart from that, they had many smaller colonies scattered throughout the war at any given time. This meant, they had landing points and outposts throughout the entire globe, and they had influence in many, many smaller countries. With the cutting edge technology, a strong government system and the fact that they had fingers all over the globe, their influence grew to the point that they could control many other nations. This was specifically true for Britain, although France did this as well.