Sorry you feel like a failure for your family, of course I don't know but it sounds to me that you are being very hard on yourself and no matter if you ever felt you fail or wasn't enough for your daughter in a moment, you always can change this. You deserve your opportunity and your child deserves the opportunity to have her father in her life.
Do you know if your daughter blames your for you and your wife separation?

Divine gave you a lot of good insight. I also disagree with what the psychologist said. One thing is not forcing a kid too much but little by little, visits even under some kind of supervision if it's needed...I know a kid has a great capability of adaptation and she will see her time with you is worthy. And you are gonna do it worthy. Don't give it up. Especially don't give up because you believe you are not a good father. Many parents have these fears and I would even dare to say that it's a sign of responsibility.
Hang in there and let us know if there's any change.

P.S.: I'm not a parent but I'm a teacher and maybe I could give you some insight with your kid, I tell you from my modest position.