Compliing @stormy's comments into an answer:
Shoot, when you plant seeds you plant a seed in a small pot such as 1 1/2 inch by 2". Putting seeds in a too large pot doesn't mimic the garden. Too much water in relation to roots to suck the water up. I'd transplant your starts into tiny pots and use a sprayer to water shallowly. No fertilizer yet. Planting seeds for starts in a too large pot will always cost starts because too much soil, too little of roots will enhance root rot and water problems. Have you added fertilizer?
And you never want water sitting in your saucer. Tiny plants only need surface water, shallow and kept moist with a sprayer. Plant in tiny tiny pots with potting soil, not garden soil. When they get large enough to start sucking up the water then you water deeply and allow to dry before watering again. This is when fertilizer is needed. Balanced. Don't use compost or epsom salts or fish emulsion, you need a simple balanced fertilizer such as Osmocote 14-14-14 extended release. Basic. Simple. Once or twice per year...
Fertilizer is not necessary yet. Light, warmth, not too much moisture but constant light moisture. Use a sprayer to soak just around the roots of the little seedling. Leave these guys alone but when you plant your remaining seeds lets try a starting pot. Not sure exactly what your kit provided but let's try to ensure a few of these seeds get a decent start. These companies count on the fact you will think it is YOUR fault and all that guilt will make you complaisant.
