Discontent has also been prevalent across the city, Celtic's fans having made their unhappiness towards the manager Gordon Strachan clear in recent weeks.
"It has been apparent at Rangers since the first game of the season, we were booed off at half-time against FK Zeta," said Smith.
"So if that is the way that people want to support the club, then fine, it's not our choice. It is a disappointing factor in the sense that, away from home, we get terrific backing, but come the home games; right from the very start of games, there seems to be dissatisfaction.
"I can't do a great deal about it. In my own case, there is a bit of bewilderment, but look at Gordon Strachan - there seems to be dissatisfaction there as well. Maybe it is the modern supporter's view of football, I don't know."
In what will be regarded as a warning from the manager towards supporters, Smith even openly contemplated the consequences if such discord remained apparent.
"It is difficult," he added. "When you are doing really well in a game that is not really the time that you need the support. It's when you're not doing well that you need the backing. From a managerial point of view, it just happens - whether you understand it or not is another thing. Invariably, if a manager brings this subject up, there is an outcry that you should be doing better, or whatever.
"At the end of the day, if there are a lot of dissatisfied supporters, then only one thing happens - a manager normally leaves. And we seem to have a lot of dissatisfied supporters at the present moment."