I was thinking "that couldn't have been further from the truth", but I am wondering if we can use it in a sentence that's happening in the simple past, since the tense is present perfect, you'd expect this expression to be used in a sentence using the present perfect tense.
I don't believe the phrase itself can exist in past tense. The phrase describes the (impossible) state of an object/comment vis-a-vis the "truth". Using the past tense forces you to locate "that" in respect to the truth, which renders the spirit of the phrase moot.
Compare "that couldn't have been" versus "that was not" the truth. Two different meanings.
The phrase works in any sentence regardless. The present perfect situates in the past and extends to the present.