The team has confirmed that Lee is likely to miss the 2014 campaign after the 27-year-old tore his ACL on the first day of organised team activities.
Lee is widely thought of as the best defensive player on the Cowboys' roster, meaning that fourth-round choice Hitchens knows he will have to up his game if he is to replace him.
Hitchens told the Cowboys official website: "Honestly, right now, no [I'm not ready]. But I will get there. It's going to take time. I've still got to get everything down.
"If we had a game tomorrow, no, but it's a good thing we don't. I have time to get better.
"Practising with the first string was a good opportunity to see where I need to be at, and I'm not there yet. It was a big eye-opener, like, 'OK, you're not where you need to be and there's still room to improve.' There is time."
Lee has missed 16 games over the past three seasons due to an array of injuries.