We can't tell you much without knowing what lens you've been using but if you want to shoot day time sports there are a few zooms which can do a good to great job but night sports is a very different thing. Be prepared to dig deep if you're really serious but if you can live with good vs great image quality (No matter which way you go there is a learning curve so allow some time to perfect your technique). On the lower end I'd recommend researching the Tamron 70-300 VC & Canon 70-300 IS. A better lens but also shorter reach wise is the Canon 70-200 f4 L or better yet (& more $) is the 70-200 f4 L IS and even more expensive are the 70-300 L IS & 100-400 L IS but it may be a bit long at the wide end for the soccer.
I think the problem is that you are zooming in BUT only slightly vs what your eyes see. That's the "kit" lens which is just a starting point for general photos and it's not considered a telephoto lens which magnifies the view much more. I suggest spending a bit of time here
seeing what the different focal length do when composing a shot. It should take a bit of the mystery out of the terminology
If both the soccer and the horseback riding are "daytime" activities (plenty of light vs. artificial field lighting) then you might want to look at the either the EF-S 55-250mm f/3.5-5.6 IS STM (and note that I bolded "STM" because Canon makes a non-STM version of the same lens which is does not focus nearly as fast. For action photography where focus distance is changing while you are trying to focus and shoot, you want a fast focusing lens. The STM seems to run about $50 more than the non-STM version, but it has nicely improved image quality and the faster (and near silent) focusing motors.)
Another lens option would be the Canon EF 70-300mm f/3.5-5.6 IS USM. The USM focusing motors are a little faster than the STM motors. And while the USM motors are quiet, they aren't quite as quiet as the STM motors (although for your activities, you wont care.) The 70-300 zooms in just slightly tighter (not a lot... just a little.)
Again... both of these options assume nice levels of available-light (daytime shooting outdoors.)
There are f/2.8 zoom lenses which collect substantially more light -- nice for indoor or night-time sports games where available-light usually isn't very good because these lenses collect about 4 times more light as compared to an f/5.6 lens. BUT... there's a considerable price jump for an f/2.8 zoom lens.
You might consider renting a lens to help you decide.
A top choice would be Canon EF 70-200/4L IS. It's a little smaller, lighter and more affordable than the EF 70-200/2.8L IS. Very fast focusing, sharp and the stabilization is a bonus.
I use both of those lenses extensively for sports, including quite a few equestrian events.
These were shot with 70-200/2.8L IS...
And this with the somewhat smaller and lighter 70-200/4L IS...
If the stabilized versions of the 70-200mm lenses are too pricey for your budget, there are unstabilized versions at lower cost. With those you will need to take care to keep your shutter speeds fast enough to prevent camera shake blur in your images.
For soccer or any field sports, you may find a 70-200mm a bit short some of the time, depending upon where you can stand and where the action is on the field. So long as light is good, you could add a 1.4X teleconverter to the 70-200mm, for a bit more reach. I use a 300mm lens on a second camera, sometimes even with a 1.4X teleconverter added to it (the combo making for an effective 420mm lens). This was shot with 300mm lens...
The EF-S 55-250mm IS STM mentioned previously is a less expensive alternative that's not going to be quite as good keeping up with the action and due to f5.6 aperture at the long end will not be quite as usable in low light, but certainly is pretty capable. 70-300 IS USM models can be another alternative. There are three versions of 70-300 with USM (fastest focusing method), IS (stabilization)... in different sizes and build qualities. In addition to the more affordable standard zoom, there are an extra compact "DO" version, and a premium quality "L" version. None of these lenses are particularly usable with a teleconverter, so hopefully the 250mm or 300mm would be enough reach or you can move closer to the action.
To shoot action like the above with your T3i, you will want to set the camera to AI Servo focus. Unless light is really good, you also may need to restrict the AF system to use only the center AF point (which is more sensitive than the other points in your camera). You have to work at keeping the AF point right where you want the lens to focus, but in AI Servo the camera will continuously track and correct focus. You won't see or hear any Focus Confirmation (that only works in One Shot focus mode), so have to learn to trust the camera and yourself.
You also might want to experiment with Back Button Focusing.... this is a popular technique among sports shooters. It takes a bit of practice, but really can help a lot (I hardly ever use any other method of focusing now).
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