Football is difficult to shoot. I've gotten decent shots even with my point and shoot at some games, but I wasn't shooting an offspring either, so the little blurriness was okay (for me).
A better lens will help, but the lenses with a smaller f stop bring about new situations you need to deal with, mainly depth of field.
Some relatively inexpensive lenses to look at are the 85mm f1.8, the 100mm f2.0, and the 135mm f2.8. These are all about $400-$500 and will improve your photo taking, but since these are primes, you'll have to move around to get better pictures and these lenses can be very clear for a small portion of the picture, so you may get a good clear shot of someone's face, but his knees might be blurry.
You can also go up to the prime L lenses. The 135mm f2.0 is gorgeous. I rented it to shoot volleyball for my son's school yearbook last week and it was very sharp and produced good shots indoors. I imagine it would be awesome outside. The 200mm f2.8 is supposed to be really good too.
Then, you can get into the prime L zoom lenses. There are various varieties of the 70-200mm f2.8 that can run from $600 to close to $2000. But, they will increase your picture taking skills. Finally, I'd think the 300mm f4.0 might be good for you. It's about $1200. It would depend on how well lit your field is, but that lens would be great for field type sports. The f4.0 is the only worry.
You might try renting a lens since they aren't too bad to rent. I got the 135 L for $45 for 8 days. You may also google canon forum and go to the first link. That place has a thread with just various examples from lenses and cameras.