We cleaned, yes, but there was that one errant shard of glass that probably got caught in between the boards in the wood floor.
I cleaned the wound and have kept it dressed and so-far haven't had any issue. If it starts to show signs of infection, I'll go to a doctor, but I washed it for a good five minutes and there was a lot of blood, so that probably expelled most of the infectious material.
It's not a particularly large wound, maybe a couple centimeters across, but it went in very deep, which is what worries me, but I haven't had any functional issues with my foot, and there's not really any pain unless I put a lot of pressure on that foot.