A 1-1 draw against Aris Limassol at home on Thursday night has left Rangers’ fate in the Europa League hanging in the balance this season.
Another draw against Aberdeen last weekend also stopped Rangers from taking advantage of Celtic dropping points in the league as well.
Thompson stressed that Clement deserves some leniency at the moment as he is yet to get an opportunity to bring in his own players in a transfer window since taking charge of Rangers.
He stressed that the Belgian has improved Rangers but feels that the last two performances must worry the Gers boss given it resembles some of the stuff fans saw under Michael Beale.
The former Rangers striker stressed that while the transfer window is not too far away, December is still massive for the Gers as they have a cup final to deal with and a massive derby against Celtic.
Thompson said on BBC Radio Scotland: “You can feel for Philippe Clement to a certain extent.
“These are not his players and he has not had a transfer window to work with.
“I think he has improved the situation at Rangers since he arrived but the last two performances have been a throwback to what we have seen previously.
“That will worry Philippe Clement.
“He doesn’t have to wait too long before he has to go back into the transfer market in January, which he undoubtedly will.
“But by that point of time, you have got a cup final, you might have been out of Europe and you play an Old Firm game that might be quite decisive in terms of where the title goes.
“It’s a huge month this for the football club.”
Rangers will push to get back to winning ways when they will be hosting St. Mirren at Ibrox on Sunday.