I wouldn't say they are lost, I would thin as normal. Then just begin pulling them slowly eating them as little babies, making room for your full sized babies. Anythings worth a try.

This is my first garden. Is the main reason for thinning carrots so that the leaves don't interfere and shade each other?
In other words, can I leave the carrots alone until the leaves start touching or are there other reasons to keep the rows 1 foot apart?

Pull them ASAP...the plants compete with each other for water and nutrients.

Leaving them an extra few days, week+ won't hurt too much, though...for whatever reason you may want to wait.

For the most part, what's going on under the soil (root space, water, oxygen, nutrients) is way more important than the top growth as far as what makes a healthy plant.

BTW...

"Pull them ASAP" sounds way more urgent that I meant...

I'd definitely shore up a little space by uncrowding them at least a bit...but you can do also balance that with another poster's suggestion of thinning some at the "baby" stage and using them.

As plant on me said 3 inches apart is perfect! but is better to start with 1.5 inches and eat the thinnings...they taste sooooooo gooood!

Do you mean the rows can be as close as three inches or are you talking about the space between plants in the same row?

If you plant in blocks, each carrot nees to be only as far apart as between plants--you don't have true rows.

In his biointensive gardening book John Jeavons recommends a 3 inch spacing (in all directions) between each full sized carrot. But since you are growing 'Little Fingers' I think they would be fine at an even closer spacing like 1 inch between each carrot. I would leave the carrots just as you planted them and then thin them to a 1 inch hexagonal spacing when they are big enough to easily thin.

The Square Foot Gardening method recommends 9 carrots per square foot (4 inch spacing in all directions) but to me this seems absurd unless you want big fat carrots. That may be nice for the county fair but really, who wants to eat big fat carrots? :( I think most people would prefer to eat long thin carrots. My experience has been that the bigger the diameter of the carrot the woodier and less edible the texture.

Here is a link that might be useful: A related thread about carrot spacing

You could thin them in a "checkerboard" pattern, so they aren't directly next to one another. That would give you extra room.

Thank you all for your suggestions and links. I think I will treat it as a "block" and start thinning to 1 - 2 inches as they grow.
I'll post back at the end of the season with results.

I plant my carrots 1.5 inches apart with rows 3 inches apart so I end up 3 inches apart in each direction and get huge yields this way... I plant in an 10x3 ft block

You could wait till they get a little bigger and transplant the seedlings so that they are more spaced out. I have transplanted carrots and they grew ok. I tend to plant seeds close together knowing I will harvest them when they are baby carrots which leaves room for the others to grow bigger.
Clare

I like to mix my carrot and radish seeds together and scatter them in my wide bed. The radishes sprout first and when I pull them out, it makes space for the slow-poke carrots.

I think the row and distance are insensible. Why space carrots 3" apart when it says rows should be a foot apart.

So I use Square Foot guidelines. All the carrots should be that same distance apart row or spacing.

Just snip the seedlings that emerge to leave the rest all 3" apart in all directions. They will do great!