Don't believe me... here's a quote from a NASA webpage:
In both the 2D and 3D cases the upflow (or upwash) in front of the wing balanced the downflow (or downwash) in back of the wing caused by the bound vortex. But, in the finite-wing case one must also take into account the Lip vortices (assuming that the influence of the starting vortex is negligible). The tip vortices cause additional downwash behind the wing within the wing span.
Here's the page it is from:
http://history.nasa.gov/SP-367/chapt4.htm
The only difference between a 2D wing and a 3D wing is vortex shedding. A 2D wing has a bound vortex that cannot be shed (there is nowhere to shed it to). Therefore, any upwash on the 2D wing MUST be matched by downwash. You may be confused by the term downwash... downwash is simply any downward component of velocity of a wing-deflected flow.
A 3D wing sheds it's vortex in the form of a wake. This vortex causes a differential downwash. Why? Because the lift across the span of a wing is not constant. The finite nature of a 3D wing causes high pressure air on the bottom of a wing to "spill over" to the top. This "spilling over" is the tip vortex.
OK, fine.... what does that mean... it means that you CANNOT shed a vortex without spanwise flow... in other words, 2D wings have no "net" downwash. 3D wings DO have a net downwash that is caused by that vortex... that is caused by that spanwise flow. No spanwise flow, no vortex shedding, no wake, no downwash.
I don't know how else to explain it. Here's a pretty picture: