Hi Sweety Cuety,
my guess is, she is your first child right?
I'm a mother of two kids. Extremely attached to me too, I credit it to breastfeeding.
Bringing my first boy to nursery for the first time was chaotic. Refused to let go at the door...
But I learned something.
So long as your child found a new friend, you can be sure that she will be alright.
Some children can click faster than others.
So my answer to your question is, be patient. dont't need to force her to play alone, continue what you do, but if you really want to start 'training' her to play alone, you should start bringing her to playgrounds, indoor or outdoor.
Sit afar and watch her play. DO NOT JOIN HER. Bring her to a playground where there are other kids too.
Through that, it teaches her social skills as well.
When you learn to let go, she will too.
No stress alright? no stress....