Meriweather was suspended for two matches, a punishment which was reduced to one on appeal, for a pair of helmet-to-helmet hits in last Sunday's match against the Chicago Bears.
The ban, coupled with a fine for a similar offence committed earlier this season, prompted Meriweather to exclaim that he would aim for the opposition's knees in future tackles, an outburst that Shanahan was unhappy with.
"I'm not sure I would have used those choice of words," Shanahan told reporters.
"Nobody's going to try to hurt anybody. But if you're going to err on the side of caution, you would rather go low than you would high.
"Brandon knows that he's got to go lower or he's not going to be playing in the National Football League."