That is correct, you get no child tax credit. 

Your income is too low.  The child tax credit  (CTC) is  limited to your tax liability. The CTC is a non-refundable credit and can only reduce your income tax to 0, It can not help you beyond eliminating your tax liability. But, if you have more than $2500 of earned income, some or all of it is usually given back to you thru the "Additional Child tax credit". That is, part of the CTC may be on line 17 of form 1040 instead of line 12.   The  ACTC is calculated on form 8812 and  is basically 15% of your earned income over $2500.  

The ACTC is a maximum of $1400 per child (not $2000).