The simplest way to get rid of aphids is to wash them off, using your fingers to help remove them, but this would perhaps be too difficult if it's not flat leaved parsley.
And the fact that it's indoors in a pot makes it more difficult.
There are lots of tips on how to get rid of aphids -
Spraying the plant, (on the underside of the leaves, especially), with a mixture of a well known washing up liquid in water, with a little bit of cooking oil mixed in does the trick, but there's the risk of a residue of soap on the plant.
Aphids apparently don't like chilli, garlic or tomato plant leaves; infusing any of these in water overnight and spraying the plant could get rid of them.
(I haven't included a link because this information came from so many different sites, but they all basically recommend the same treatments.)
But, what I would do, to be able to access all of the aphids, and to be able to thoroughly wash it afterwards if using the washing up liquid cure, would be to carefully uproot the infected plant, (keeping as much compost/soil on the roots as possible and gently wrapping the roots with kitchen roll to prevent the compost falling off, or damaging them, then swish the plant around, upside down, in any of the above solutions.
Use your fingers to dislodge the aphids, but if using the chilli solution, it might be best to wear rubber gloves,
If it's too difficult to remove only the parsley from the pot, you could remove them all and re-pot them all afterwards.
When you've successfully removed all the aphids, as they don't like coriander, pop a couple of plants of this in the pot also, to prevent a further infestation.
P.S. I haven't actually done this myself, as I haven't had this problem, but I'm confident that you won't harm the plant.
If you do I'll sent you a new one.