Some background, and then some thoughts on your specific problem.
The way that I tend to approach my thinking about exposure is that there are two factors that affect exposure: 1) amount of light coming in through the lens and 2) sensitivity of the medium. In turn, amount of light depends on a) illumination (whether flash or ambient), b) aperture; and c) shutter speed.
As a result, the exposure depends on four factors: ISO, f/stop, shutter speed, and amount of light available. I think of it this way because you can also adjust the amount of light available, whether it is turning up the rheostat on a continuous light, increasing strobe power, opening up curtains and shades or scrumming off sunlight, etc.
We think of aperture as being the controlling factor for strobe light because, as has been noted, the strobe duration is (in general) much shorter than the shutter speeds we use, and so effectively changing the shutter speed over any range at which the shutter is entirely open for the full flash duration does not affect the exposure. Nonetheless, you still factor in shutter speed when you are a) using auto-FP, b) your shutter speed is actually faster (shorter duration) than the strobe, as is the case, for instance, when you use an SB800 at full output (1/1) and a shutter speed of 1/2000 sec; the flash duration (excepting the trick of auto-FP) will be longer than that shutter speed.
My usual approach is to select my aperture based on desired depth of field, titrate shutter speed appropriately for the ambient to whatever effect I am looking for (in your case, include the background and saturate colors, but of course I might go to my max sync speed if I am trying to completely eliminate ambient and separately light a backdrop or have the background go to black) and then titrate flash output for the correct subject exposure.
Now, to your specific image. Given that the subject is underexposed from what you were trying o achieve, there are a number of potential causes and figuring out which one requires a bit more data as to flash mode (TTL, TTL-FP, manual, AA, etc), location (on camera, off camera, controlled by a SC-28 sync cord or CLS), etc. If you post this info, we can give a bit more help to you.
Possible explantations: 1) Your strobe may not have had enough power to achieve the proper exposure at your programmed ISO/aperture/shutter speed. In TTL mode, a Nikon speed light will beep multiple times to indicate underexposure. The solution could be to use multiple strobes to increase power output (this gets expensive if you need more than one stop of power, though - to increase power output by 2 stops, you need 4 flashes, and so on). Another solution as was suggested is to increase your ISO, and then you can adjust shutter speed to correct ambient. You could also switch your light modifier as using an umbrella and/or soft box can cost you 1 stop or more of light. You can bring the strobe closer as well, but again that changes the character of your lighting.
2) If you are in TTL mode with matrix metering, the bright sky may well be fooling the matrix metering and lead to underexposure of the subject. While the Nikon speed light/meter system usually does a good job of figuring out these situations, it is not perfect and in TTL mode I often do wind up tweaking the flash exposure. TTL-FP (which is the fill-flash mode) helps to address this, but sometimes Nikon's computation of the proper fill is not what you would want either.
3) If you are shooting entirely manual, and have used a light meter to set ambient exposure and flash exposure, then the problem is that you are exposing "correctly" for the meter, but not correctly for your desired outcome, and here again is a situation where the artist takes over from the numbers.
If you post more info on your setup, I can try to help more.