It's not until they are older, that they will "realize" that to get more liquid they must "tip" the sippy cup.
Just keep showing her how. They will get the hang of it.
OR, use a straw cup for her. Some kids like this better, each child being different. You don't HAVE TO use a sippy cup.
Either way, you are not getting her "stuck" in a habit as a "crutch." As they grow up, they will NATURALLY be able to drink from ALL sorts of things. Don't worry. This is just a part of their development. ALL normal. You don't see grade school kids drinking from a sippy cup, right? They drink from all sorts of things. It's all simply a part of "ages and stages." That's all. Don't get hung up on what kind of "spout" they drink from... main thing is they can drink. Then, they will naturally, in their own time, transition to other kinds of spouts to drink from. It's a natural progression. No worries.
I would NOT lay her on her back to drink... this can also trigger ear infections in some children.
Until she is older, yes, you will need to help her drink from the sippy cup. This is normal. Once she gets her motor skills and coordination, and cognitive skills and abstract reasoning, and cause/effect developed more at an older age, then she will be able to do it herself. Each child is different in the pacing of their abilities. It's okay, your baby is normal. This is normal.
All the best,
Susan