If you're stirring in circles, you're not whisking. A proper chasen (bamboo whisk) should be moved in a quick zigzag or 'W' motion, which aerates and breaks up clumps. Also, don't press too hard—let the whisk do the work.

Fix: Use a chasen if you have one. Start with a small amount of water, whisk in a zigzag until smooth, then add the rest.