First, welcome to POTN.
Next, there's a lot to learn and not much time, so I'll give you the highlights. When in one of the "icon" modes, or basic modes, the camera guesses what you want, and may guess very wrong. The "night" setting you refer to is probably optimized toward long exposures in low light, leading to the motion blur you're seeing.
Closer to what you want is the "running man" icon, which is a guess at what your might want for a sports shot -- higher shutter speed to reduce motion blur. Neither is really the best option, however, as you leave too much up to the camera to decide, and it can only guess at what you really want.
In either case, the basic modes are just the camera guessing at how to take the picture you want. It's limited in what it can do on its own. I think the basic modes are limited to ISO 400, while your camera is capable of ISO 1600. ISO 1600 will give you a shutter speed 4x as fast as ISO 400, doing a better job of reducing motion blur at night.
Your lens will also be a limiting factor, as you likely have what is commonly known as a "slow" lens. A slow lens is one with a relatively small maximum aperture, meaning it is capable of letting in less light than a "fast" lens (something with a maximum aperture of f/2.8 or better).
Taking pictures is a balance of ISO, shutter speed, and aperture. A faster shutter speed requires a larger aperture, and particularly at night, a faster ISO. To get a faster shutter speed, you'll need to have a higher ISO than the basic modes allow.
Move to one of the creative modes on your camera (AV, TV, or even P in a pinch), and set your ISO higher. For night football, you're likely to need at least 1/250th at an absolute minimum, with 1/500th or faster even better at stopping motion. Your equipment may not be capable of reaching those speeds depending on the amount of light available at night.
In AV mode, you control the camera aperture and the camera chooses a shutterspeed to match -- so set it to as small a number (which means as large an aperture) as your lens will allow and see what kind of shutter speeds you get.
In TV mode, you control the shutter speed and the camera chooses an aperture to match. Crank the ISO up to 1600 for night spots, set a shutter speed of 1/500th, if you can, and see if that works any better.
Others may suggest M, for manual, but at this point it doesn't sound to me like you have enough understanding of the relationship between ISO, shutter speed, and aperture to make that leap.
I know this is a ton of information, and quite likely sounds like a foreign language. The best I can say is to experiment, and get out of the basic modes so that you can begin to tell the camera what you want, and not rely on it trying to read your mind.
Good luck, have fun, and be prepared to make mistakes as you learn. Stick around here and you'll learn a lot.