There are proper tools for this job, but you're in a hurry. Jam a pair of long needle-nose pliers down the hole. Have thier jaws open enough to straddle the strainer. Use this like a back up wrench and tighten the nut with a pair of channel locks/pump pliers. Hope you used plumber's putty. Good luck!
PS If you need more leverage on the needle nose pliers, grip the handles with a crecent wrench.