"Quick Align", I believe, just assumes the mount is aligned properly to the North Celestial Pole, and that the mount is level, and that it's started exactly on the index marks. My guess is that you're close, but not exactly there. This can be due to a number of possible causes, but if you take a step back, there are actually two kinds of alignments that you need to do: Polar Alignment, and Sky Alignment.
So the first thing, before you even turn on the mount, you need to get the axis of the scope aimed exactly at the NCP. It's near (not exactly at) the star Polaris. With the overall telescope aimed north, loosen the upper clamp and turn the telescope to the side (90 degrees). Remove the cap in the front, and unscrew the cover in the back, and you'll see a hole that runs up the middle of the mount. That hole needs to be aimed at the NCP. Normally a Polar Alignment Scope would go in there, but I'm assuming you don't have one yet. For now, try to adjust the knobs on the mount to put Polaris in the middle of the hole, as you sight through it. (In reality you need to be more accurate than that, but this should get you close.) If you have a smartphone, there are a number of apps dedicated to helping with a Polar Alignment, and will show you where Polaris should be, such that the NCP ends up in the exact center.
Since none of the positioning is exactly correct (microns count in this hobby), you still need to give the scope a dose of reality as to where things actually are in the sky. That's the second alignment. Once you do the Quick Align, tell the scope to go to a bright star you recognize in the east or west, about half way up in the sky. It's going to miss, as you noted. Use the hand controller's arrow buttons to move the scope so it's pointing exactly at that star (centered in the eyepiece), then go to the "Align" button and set it as an alignment star. Do that again with another star on the other side of the sky. That lets the hand controller update its model of where things are, and now a goto operation should be a lot more accurate. If you have a smartphone, find one of the several night sky apps that let you aim your phone at the sky, and it shows you what you are looking at. I'm using "SkEye" on my Android phone, but there are several others. (Essentially what you're doing in this is a "Two Star Align", but you pick the stars that you recognize, instead of the telescope picking stars that you don't.)
Best is to do this yet a few more times, adding those stars in as "Calibration" stars, under the Align button's menu. Two alignment stars, and 2-4 calibration stars should get you a goto that lands pretty much dead center in the eyepiece. It does take a little practice, but in time you can do this pretty quickly.
A challenge in this is determining where the "center" of an eyepiece is. If you can, get an Illuminated Reticle eyepiece, and use it's cross-hairs to exactly position the star.
It helps to use the Motor speed control ("9" on the hand controller) when moving the scope by the hand controller. I use speed 7 for initially moving the scope, and speed 4 when fine-tuning it through the eyepiece.
Another thing I recommend is to get a "Telrad" finder. It's a lot easier to use than the magnified one that comes with the telescope. A Polar Alignment Scope also helps getting the mount exactly aligned with the Earth's axis, instead of guessing at it through the hole.
I started out just as you are, and came to realize that finding stuff in the night sky requires a degree of precision that's hard to get without additional tools, and especially some practice using them. But have fun with the new scope!