Welcome to the forum.
My first advice is to avoid the 'picture' settings. They are just there for people who don't know any better...and they really don't do anything that you can't do with the four primary modes (P, Aperture Priority, Shutter Priority & Manual).
Getting back to your question. The sports mode simply puts a priority on a faster shutter speed...but the shutter speed that you can use, is determined by the light that you have to work with...and is limited by the lens's maximum aperture and the ISO setting.
So in other words, you just didn't have enough light to get sharp shots, given the aperture of your lens and the ISO setting.
I'd guess that the lens was at it's maximum aperture, so your only option there would be to buy a new/better lens with a larger max aperture.
You might be able to turn the ISO up higher, which would allow you to use faster shutter speeds...but the trade off is more digital noise.
Lastly, you could add light. Either by using flash (or another light source) or by shooting where/when there is more natural light.