7D Picture Quality...user error?

Hi,

I'm getting back into photography and would appreciate some advice on a few pictures I've taken. Hoping these aren't stupid questions!

The shots below were done with EF-S 15-85mm f3.5-5.6 IS USM lens.

I've taken others with EF 70-300mm f/4.0-5.6 IS USM and obtained similar results.

Using DPP the focus point was the lead deer. I ran into them when driving to the cottage and didn't have time for a tripod so they were free hand. And, I didn't take time to setup as I was concerned they would take off.

When I zoom in and use Elements to make some corrections they aren't as crisp as I would have hoped.

So, is this because I didn't have the correct settings? Or, is this something else that I should look into?

I've read a number of posts on the 7D sensor and would like to understand if what I'm getting is expected and I need to do more post work or I screwed up and if I did what should I do moving forward. Other than likely increase the shutter speed as it may be too low but the deer were statues.

Thanks,

-G