Lyle Taylor had put the visitors ahead after just five minutes before 22-year-old Routledge levelled on 42 minutes.
And despite the result keeping his side ninth in the Irn-Bru First Division, boss Billy Reid was not upset at having to settle for a point.
"It's taken a lot of time to get the squad together but it showed against Falkirk that they have not played a lot of games together," he Reid.
"We are still a wee bit fragile at the back. We've had a lot of good play, a lot of smashing play.
"There were pleasing aspects for us and we will get better. I've been saying that all season, and I still believe it.
"We still have two or three players who have fitness problems and once they are back we'll be a bit stronger. We showed character."