Carrots are finicky in that they take a while to germinate and the soil needs to stay evenly moist. Some people use old burlap bags to cover them while they are germinating. Here's a kind of tutorial:http://www.ericamulherin.com/blog/2011/ ... ng-burlap/
Another option to think about if you decide to plant another row later is that some people alternate the carrot seeds with radish seeds to help mark the row (radishes are fast sprouters) and also to help break up any crust that may form in the soil from keeping it damp.
I have never direct seeded tomatoes, but I have had many volunteer. I think they are a bit easier than carrots, so you shouldn't have any problems with them. Good luck!