Debutant Paul Rutter gave Blues the lead after 19 minutes but Drayton's Paul Bowyer equalised on the hour.
The result keeps Blues eleventh in the table, nine points behind leaders Chasetown.
Today's team:
1. Steve Hodgson
2. Matty Johnson
3. Paul Taylor
4. Andy Taylor
5. Nick Ward
6. Mark Ruddock
7. Dan Cope (15. Paul McMahon)
8. Rob Hawthorne
9. Paul Rutter (12. Ashley Miller)
10. Dean Crowe (14. Leon Ashman)
11. Wayne Corden
Unused Subs: 16. Pete Johnson 17. Wayne Johnson
Yelloe/Red Cards: Andy Taylor, Nick Ward, Rob Hawthorne, Paul McMahon
Attendance: 251
See match reports section for Mike Cope's report.