I agree - as a native English speaker, "I feel it's difficult" seems more correct to me.
Here is the important difference. When you say "I feel difficult", you are saying that it is "I", the speaker, who is difficult. This is probably not what you meant to say. Saying "I am difficult" might mean that you are unhelpful or uncooperative!
When you say "I feel it's difficult", which is the same as saying "I feel it is difficult", you are saying that "it" is difficult - "it" refers to the next part of the sentence: "to keep exercising".
In the first example, "I" is the subject.
In the second example, "it", or "to keep exercising", is the subject.
I'm not a professional teacher, but I hope this helps you!