Martin has won five, drawn five and lost five with Rangers, with away trips to Sturm Graz in the Europa League and Falkirk in the Premiership coming up.
“I do think they’re going to have to go on a big run to try to change the narrative,” said Thomson, who won five trophies during his time at Ibrox.
“When that narrative comes, and fans have had enough, it’s really difficult to turn.
“He [Martin] says it constantly: the only way they can turn it is winning games. They’ve got that win now, can they build on it? Thursday night is obviously going to be a difficult one. Falkirk are probably one where if you were picking another team, you would hopefully fancy your chances. At the same time, I don’t think any game is easy for Rangers at the moment.”
The icy reception to three points in Livingston suggests that simply winning may not be enough though.
“You can play really poorly (and win) and the narrative can still be one of frustration,” added Thomson.
“The fans expect more. They want to see high-energy football, the stuff that the manager promised when he came in.
“When that is not met, and it falls short, especially added to poor results, you naturally come under pressure.
“I hope Russell does a good job, I hope he turns the corner and that there can be some sort of run and that the fans can get behind him.
“It’s certainly volatile stuff to watch, the reaction of the fans. I think it will be a difficult one for him to turn around.”