I accidentally deviated from an ATC instruction as a student pilot. How bad was it?
Well, you screwed up, but nobody got hurt, no metal was bent, and since the tower didn't yell at you presumably you didn't obviously endanger anyone's safety (though there's always some level of risk when an aircraft isn't where the tower expects it to be).  

As far as deviations go, that's not good, but it's not terrible. The tower was probably expecting you to report 3 miles out, continuing in to about a mile from the field for your downwind.

Schedule an extra half hour of ground time with your CFI before your next flight to talk about what happened. Also take the time to fill out an ASRS report explaining what happened and why (It's probably unnecessary in this case, as a student the tower will almost certainly be satisfied with you getting "a good talking-to" from your instructor, but it's a good way to learn how that system works.)



There are a couple of other things you might want to do on your next few training flights:


Spend some time getting comfortable in the pattern on windy days.
You should be comfortable in a tighter pattern than 3 miles, even on a windy day (see my next item for why). This takes practice, and fortunately for you it's spring (at least in the USA) so there are plenty of windy days in most of the country!
Practice some engine-out approaches to get a feel for your plane's glide performance.
A base leg 3 miles out in a typical GA trainer is very wide -- Remember you generally want to be able to make some spot on the runway if your engine quits on downwind, and you probably can't do that from 1000 feet AGL at 3 miles out.
Take a few laps around the pattern and have your instructor pull the power at various points so you have a feeling for how the energy management works out - this will give you a good feel for how wide your pattern should be.
Turn the GPS off and practice flying visually.
The GPS is one link link in your error chain, but I think it's a big one: If you were flying visually and relying on landmarks to judge your distance rather than the 3 mile alert from your GPS you might have realized "Hey, I'm entering downwind - I should tell the tower!"