I can see what you mean, but inflation is just the rise in the price level, which can be caused by increases in the money supply, but also by a fast-growing economy. So inflation can cause depretiation against other currencies like you just said, but only if it's the result of an increase in money supply.
I think the main reasons for the low value of the dollar are the trade deficit and the low interest rates. Americans are importing more than they are exporting, so they give dollars to foreigners, or trade them away for the necessary foreign currency. The low interest rates mean that noone wants to keep their dollars, and trade them for other currencies. Thus, low demand.