Can you be given a disadvantage on a saving throw if you are surprised?

I have an odd inquiry, this happened during a D&D 5e session. We were travelling in a cavern hunting a necromancer, as myself and a party member parted to a path further exploring away from the group. We were then apparently disadvantaged on a Wisdom saving throw regarding a spell or (something), because we had no idea it was happening.

I had my Dark One’s Own Luck with my level 6 warlock, and was told that I couldn’t have used it but because I was surprised by a spell, and I had to “call my patron”, and I was not told I was disadvantaged. As such I was unaware that I was even being disadvantaged to begin with and presumed my positive 19 roll on a DC of 16 succeeded when in fact it failed as my disadvantage roll was 15.

Is such a thing even possible, or was I correct in the assumption such a thing can’t happen?