Thinning the lettuce you can make baby lettuce salads and they are REALLY good... my favorite is the first thinning of the season... they are so tiny and crisp. Pull them up roots and all, and then take the roots off and throw them in a salad spinner.
Well thinning carrots may not be such a good idea... honestly... I would just leave them. Carrot flies are attracted to the smell of thinning carrots and they then lay their eggs in the left over carrots. When ever I would pick my carrots I would throw the carrot clippings in the compost (all the way across my yard and down the hill) and then water my carrots heavily (to reduce sent) and I still sometimes would end up with carrot flies. Carrots do not replant well... their root structure is the basis of the plant. It is your call but I would leave them alone, and plant the seeds farther apart next year.
All in all do not feel bad... Think of it this way... the only way your baby plants are going to reach their full potential is to take out some of the other plants. If you eat them they are not going to waste and it is worth it to have lots of salad all year instead of one huge harvest at the end of unhappy crowded plants.
Love Val