No, we won the war in Iraq. The idea now is to win the peace, i.e. do not allow dictatorships enslaving and killing millions of people to re-emerge like we did after WWII.
I guess the difference between then and now was that no one ever said we "lost" World War 2 just because the postwar situation was less than perfectly-peaceful, free, and idyllic.
But nowadays, in order to "win" a war we must make the postwar situation completely violence-, crime-, and unpleasantry-free. If we don't, we "didn't win", or "lost the peace", or even "lost".
But of course, this standard of "winning" is impossible to meet, which was my point. According to this standard, we didn't win World War 2, or any other war.