This is most likely the result of over watering or the soil having too heavy a water retention quality. If roots are not able to breathe oxygen, many symptoms of nutrient deficiency surface.

Soil in the picture looks very dry. Watering (usually too much) is a common problem, but too little is also a problem. You have to find the happy middle ground.

FataMorgana

Yes the soil on top come really dry, thats why I water them every 2 days .. I don't water them a lot though

Over watering, if the soil has drainage is not a problem with parsley. I have a 15 sq-ft bed of parsley, over wintered in PNW wet winter and now it rains almost every day. They are lush green now.

I suspect lack of water and lack of nitrogen. Parsley is a leafy green and benefits from some extra nitrogen.

ALSO

No I started them, so you are saying that parsley can tolerate a lot a water when there is a good drainage ?

You have to find that happy middle ground - not too much and not too little water. Your plants will tell you if there is to much or too little water. If you are really unsure, opt for too little first and then increase as needed. Since I suspect you've been in the too little category, you can increase the water.

-FataMorgana