Walter Smith is concerned about the possible fallout from a recent fans' protest against the Rangers board.
Supporters have called for club owner Sir David Murray to step down after growing increasingly frustrated at the direction the club are heading.
The 'We Deserve Better' campaign has been condemned by the Rangers Supporter Assembly, the umbrella organisation representing the club's followers across the world, but continues to remain in the public eye.
Smith fears further protests will be staged during the Gers' SPL clash with Falkirk on Saturday and admits the continued ill-feeling brewing in the stands could prove detrimental to performances on the pitch.
"If people are unhappy with the way we're going, they've got the right to express that disquiet," he said.
"I just hope it doesn't affect us too much. There is an awful lot going on around the club at the moment.
"So far, I don't think it has affected anything on the footballing side of things and that's the most important aspect from my own point of view.
"If there is going to be a protest tomorrow, I'm not quite sure how many people actually support those who have been critical this week.
"If it's a huge element of the support then obviously we will have a problem that we will have to overcome. Hopefully, it won't affect anybody on the pitch.
"I'm sure if we go out and play well enough then we can quiet them a little bit. We just have to keep trying to win games."
Meanwhile, Smith has dismissed reports linking Kris Boyd with a move to Lazio and highly-rated teenager John Fleck with Manchester United, Arsenal and Tottenham.
"We've not had one enquiry for any of our players at the moment," he said.