According to traditional grammar rules, after the verb “to be” we need a predicate in nominative case (ie. This is she. It is I.) and so “It’s just you and I” is correct.
But out here in the real world, almost everyone feels more comfortable with the idea that after a verb we use objective case, so we say, It’s me, and “It’s just you and me.”
So now that you have the facts, you have to decide: Do I want to sound like a grammarian, or do you want to sound like a normal speaker of English?
I think both are correct. But the use of "me" instead of "I" is more common. For example, "It is I" is not commonly used now but before, was considered more formal and precise. Nowadays, "it is me" which is common.