How do you bring a child into the world without your world being consumed by their needs? Give them a sibling so they have each other! Get them a dog! (Just kidding.)
The answer is, you don't. Parenting is a full time job, and the time you put in now will pay you back when she becomes a strong, independent functional societal unit and still loves and respects you.
That doesn't mean you have to be at her beck and call. It doesn't mean that there shouldn't be activities that she can do quietly. However, it does mean that her needs come first (and here I think I'm sensing some resentment on your part for painting your child in a childish and immature light - she often turns on the waterworks and goes crying to mommy - yes, that is what childish and immature 4 year olds do. They act like 4 year olds.)
You do deserve credit for the things you're doing right, and I admire you for them. You're probably drained at the end of the day and would like to rest some. So what do you want to do? If it's an activity like gaming, then you just need to set priorities. Figure out what is more important to you than your daughter, and do it without feeling guilty. But if you do feel guilty, there must be a conflict in there somewhere.
I don't know your home situation. If your wife is a stay-at-home-mom, she needs a break from your daughter, too.
There are chunks of time that should be your own (away from work), but these should be a small percentage of your time right now. Then there are chunks that should be just your wife and you - a larger percentage of your time. The rest is with your family.
You need to find a balance between doing things with her that you feel obligated but unfulfilled doing (perhaps like playing with stuffed animals or playing Candyland) and doing things that you both like doing (there are some terrifically good children's books out there), outdoor stuff, sedate stuff (kid's movies), etc. Maybe you can do something else while you're attending to her that is shared and fun for you: photography, or art. But it all matters to her. Make it count, be present, impart values to her while doing stuff together.
As she gets older, there will come a time when she will want to shut you out (hard to imagine right now, right?). There will come a time when she will be embarrassed by you, and will even think you don't know anything. It happens with almost all kids.
When that time comes, you'll probably reflect on earlier times and think, what did I do wrong? Everyone goes through some degree of that. The key is to have an answer that is acceptable to the future you.