If you are worried about needle contamination, you should be fine. I once sleepily put the uncapped syringe on the kitchen floor, before giving the shot--and Cliff ended up being fine.*
(I did worry and stress and googled "needle contamination" and posted here... and in the end, I just kept an eye on the injection site to make sure there were no signs of infection, and moved on to the next day.)
*This is just my experience. I'm just sharing something that happened to me, and turned out fine, but I am not a vet or medical professional! Please don't beat yourself up though!