Side note: I think you forgot the word "not" at the beginning of the second clause of the second sentence. I'll assume that, anyway.
The two sentences mean different things. The word "felt" or "feel" in English can have two very different meanings. One, it can mean that you sensed something physically. Like, "I felt his hand on my shoulder" or "When I stepped out in the rain I felt very cold." Two, it can mean that you had an opinion. Like, "I felt that President Jones did a good job while in office" or "I felt that Sally was likely to win the science fair."
My first impression of the first sentence is that it has meaning number one. "I felt her tilt her head back" sounds to me like you are saying that your hand was on her head and you could feel her tilting her head, or perhaps that when she tilted her head back she bumped into your shoulder, or some such.
The second sentence sounds like it's expressing an opinion. It is my opinion that the reason why she tilted her head back was to look at me.
The word "that" makes the difference. When we are talking about an opinion, we generally say "felt that" or "feel that". "I feel that this is a good idea." When we are talking about a physical sensation, we usually don't use that. "I feel cold", "I feel tired", etc.
But it's not that simple, unfortunately. Often we decide which is meant based on context. If you said, "I feel Sally is going to win the science fair", well obviously winning a contest is not something that you would normally determine by physical contact, so a reader would assume you meant to express an opinion. "I feel that it is cold today" is odd wording, but I think people would take it to refer to the physical sensation. But then, "I feel that it will be cold" is clearly an opinion and not a sensation. Arggh, language can be complicated!