Darth Sidious had seized control of the Republic and reformed it into the Empire by the time Yoda confronted him. He was, in effect, in command of the entire galaxy, with a loyal, brainwashed clone army at his disposal. To free the galaxy from the grip of the Emperor, Yoda had to defeat him. A draw wouldn't be enough because Palpatine would stay in power, and the Jedi would remain in hiding. To restore balance, Yoda had to win. In the end, the two were evenly matched, and so although the Jedi Master wasn't defeated, Palpatine remained in power. Thus, Yoda considered his mission a failure, realizing he wasn't strong enough to topple the Sith Lord.