they can't think like us 可以理解为 they can't think like we think/do 的缩略.而as在表示"像"这个意思时,一般是用 as (adj/adv) as (sb.do)/(adj)的形式.比如as soon as possible,as well as we do等等.
这个句子不能用they can't think as us,但可以说 they can't think in the way as we do,或者 they can't think as quickly/thoroughly/deeply/naturally as we do.