Pierce, who recently joined the Nets following a 15-year spell with the Boston Celtics, claimed that it was time for his new side to "start running this city" in an interview earlier this month.
Smith took exception with those comments and told ESPN: "I just look at him as a bitter person just getting out of Boston. He doesn't really know what New York is all about. He has been playing in Boston his whole career.
"He just knows, just know that his words have consequences and he's going to have to pay for them."
The two sides will meet for the first time in the season on December 5 at the Barclays Center.