It's always easiest to blame the gear when there appears to be a problem... But that's usually not where the fault lies.
It is possible the lens is faulty... out of calibration or has a de-centered element. But these issues are rare.
The EF-S 55-250mm is not known to be a "problem" lens... actually is quite good for the money (even if rather lightly built, i.e. "plasticky" )... especially in the two most recent "IS II" and "STM" versions. I didn't see any reference to which version you have... But these two latest ones are both currently available and improved upon the original a little bit in terms of image quality. The STM version basically is the latest and greatest with little changes from the IS II other than it uses a modestly improved (quieter and smoother) autofocus drive system.
Most common problems are user errors or poor/incorrect techniques...
1. Do you have a "protection" filter on the lens? If so, remove it and try the lens without it. Also spend a few $ for the proper, fitted lens hood. The hood will do a better job protecting the lens, can't hurt actually might even help image quality, and may even help auto focus performance. If you must use a "protection" filter, get a good, multi-coated one.
2. All versions of the 55-250 haves IS so you can use a little slower shutter speeds so long as you leave IS turned on. Without IS, on your camera you'd actually need around 1/400 minimum shutter speed to handhold a lens at the 250mm focal length setting. People differ in their ability to hold a steady shot... so you might be able to get by a little slower with care, or may need a faster shutter speed if your hands aren't very steady.
With IS on, you should be able to handhold it at 1/100, maybe even 1/50, as far as camera shake is concerned.
However, IS cannot do anything at all to prevent subject movement blur. You are going to need 1/400 or better to stop the movement of feet and the ball shooting soccer. I'd try for upwards of 1/500 or 1/640 or 1/800, to be sure to stop movement... faster is better so don't be afraid to use 1/1000 or faster if possible.
Out in broad sunshine I'd recommend ISO 400 or 800... in shade or on a fairly overcast day, use ISO 1600.... all to be sure your shutter speed is fast enough to capture action shots.
Inside and for night sports photography "under the lights", even higher ISOs help (3200 and 6400), but these always require more work in post processing to rein in image noise. I'll only shoot RAW, am very careful to avoid underexposure and plan to do a little to a lot of extra work on the images after the fact. Generally speaking much more expensive and heavier gear is needed, too... f2.8 and faster lenses for example.
3. Shooting too fast, not allowing autofocus time to acquire the subject or trying to track fast moving subjects adds difficulty. A USM lens is both faster acquiring and better at tracking movement. USM focus drive becomes even more important in low light situations.
4. Too much automation... setting the camera to the "Sports" scene mode, I have no idea (never use it) how this sets up autofocus, what shutter speeds and ISO the camera forces/limits you to use, etc. I know it will allow JPEGs only and am betting it puts it in AI Focus mode and All Points/Auto Selection pattern, neither of which I will use for sports photography.
When I'm shooting sports I use AI Servo and Single Point/Manual Selection. This way, the camera and lens operate as quickly as possible and do their best tracking moving subjects, but I have to do my part as the photographer and keep the AF point (usually just the center one, which is more sensitive than others on many Canon cameras) right where I want the camera to focus.
I also use Back Button Focusing, to separate focus from the shutter button and puts AF more fully under my control. It takes a little practice, but soon becomes second nature to use this technique. It's especially popular among sports photographers.
http://www.learn.usa.canon.com/resources/articles/2011/backbutton_af_article.shtml for more info.
5. Massive over magnification of your images when viewing them on your computer is another common mistake. The T4i is an 18MP camera. If you view images at 100% on most computers monitors, assuming that the monitor is set to it's native resolution, that's like viewing the image printed five feet wide, from about 18" away. (The Ken Rockwell article linked above is pretty old now, referring to 2006 image resolutions and some other now-defunct technologies.)
Back off to 50%... or to the actual size you'll be printing which will probably be more like 33%, 25% or even less. Zoom in to high magnifications for retouching, if needed... but not for image evaluation. You can end up simply looking at the image too enlarged, and thus be overly critical of it.
Digital images typically need some sharpening, but that usually should only be done once the image has been re-sized for it's final, intended use.
6. If every image you look at appears soft... it might be your computer monitor. There are different qualities among monitors, too. Consumer grade monitors aren't all that great (not to mention they usually are off on color and way, way off on brightness, too). I use a graphics quality IPS monitor that's great for photos (but lousy for games!)
7. Using auto focus well takes some practice. Watch the three videos beginning with this one
http://www.bhphotovideo.com/explora/photography/tips-solutions/look-canon-autofocus-system-part-1 to learn how it works. I don't believe your camera is mentioned, but the 50D is and it's AF system is virtually identical to what's in your T4i.
After viewing those, it will take some practice.
You'd do better shooting sports action with USM lenses (faster focusing and better tracking), but should be able to do pretty well even what you've already got. IMO, the minimum cost of "stepping up" is a Canon EF 70-300mm IS USM at about $650. That would be a good "daytime" lens. If you want to shoot sports in lower light (indoors or evenings "under the lights" ) you'll need a lens with larger aperture such as EF 70-200/4L IS USM ($1300) or, even better, EF 70-200/2.8L IS II USM ($2300). As you can see, the "cost to play" goes up rapidly, as the shooting situation gets more demanding!
Avoid "micro motor" Canon and third party lenses for any sort of action photography. The Canon EF 50/1.8 is the company's cheapest lens and may be fine for portraiture, but it is lousy for sports. It's AF is too slow and erratic. A Canon EF 50/1.4 or 85/1.8 each cost about 3X as much, but both of them have USM that's faster focusing and much better tracking.
Only blame your equipment once you have eliminated all the other possibilities.