Martin, who was only appointed in June, has won just three of his opening nine games in all competitions, the worst record of any permanent appointment in the club's history.
Rangers go into next weekend's clash against Glasgow rivals Celtic already six points behind the Scottish champions after just three games.
Teenager Findlay Curtis came off the bench to rescue a point for the visitors, but Martin's approach will be questioned after starting without a recognised striker.
The Buddies got the better of four meetings against Rangers last season and were on course for another famous win when Jonah Ayunga raced through to beat goalkeeper Jack Butland on 33 minutes.
Martin changed tactics and personnel in the second half, and in the 78th minute, 18-year-old substitute Curtis drilled in the equaliser with his third goal of the season.
Rangers also have a mountain to climb if they are to qualify for the Champions League, as they trail Club Brugge 3-1 ahead of Wednesday's second leg in Belgium.
To compound Martin's issues, he revealed after the match that forward Hamza Igamane refused to come on as a second-half substitute, with speculation linking the Moroccan with a move away from Ibrox before the transfer window closes.
"The issue is that the window is still open and there are people with one eye out and one eye in," said Martin.
"There are too many people uncertain, and we have to make sure we have people that want to be here."