Just to add something else (although chocolatedog's suggestion is a lot more practically helpful

) I found that I tended to bring out the hand that I was thinking about, and could actually bring out a different part by consciously concentrating on that hand rather than the other and it just happened. I don't know if it's usually the case that this works. I'm therefore going to hypothesise, although I may be completely wrong, that you're having to concentrate harder on actually being able to play the left hand than the right. If you are finding that you need to concentrate on the left hand much harder then it may be worth trying to practise it a bit more on its own and then trying to focus more on the right hand when playing hands together.
Another technique to use is 'ghosting' play the piece hands together normally but instead of pressing the keys down with your left hand just touch them or depress them ever so slightly, but not enough to make a sound (play the right hand as normal). This will get you used to going through the motions of playing the left hand without actually using much force. Then, when you're used to that try playing hands together normally again but remembering the gentle pressure.
You could also try playing something you know really well and that is quite simple: like a scale for example to use as an exercise, playing one hand quietly and one loudly

. Finally, don't worry about it too much, these things are part of the skill of playing the piano, and may take time to develop, so as you suggest just keep persevering and you'll get there

.