Yes it is correct, we often omit "like" in examples like this.
Maybe it's better for you to think about it like we know it is there, but it's not necessarily understood. We understand it as if it was present in the sentence.
Hi, I'd like to ask this question again, as I have just heard "I feel such a fool" on Fry and Laurie Reunited. Is "I feel such a" without the word "like" really OK to use, or is it colloquial like "I got to go" instead of "I've got to go"?