"We were listening to the Patriots radio broadcast for the majority of the first half," Coach Mike Tomlin said.
Other teams have reported problems with headsets at the Patriots' home field.
The Patriots have been repeatedly accused of bending the rules to gain an advantage over rivals.
A league spokesman initially said the interference at Thursday's game, which opened the league's season, was "caused by a stadium power infrastructure issue, which was exacerbated by the inclement weather".
But Mr Tomlin told reporters that he and his staff "always" have issues with the communication systems at the Boston-area stadium.
The Patriots said they had problems with their headsets as well. The Patriots defeated the Steelers, 28-21.
Sports bloggers have started calling the dispute "Headsetgate", an allusion to previous Patriots scandals dubbed "Deflategate" and "Spygate".
Last season, the NFL found that the Patriots purposely deflated footballs during a playoff game to gain an advantage. Deflated footballs are easier to throw and catch.
The team's quarterback Tom Brady was implicated in the scandal. However he successful appealed against a four-game suspension, which would have began on Thursday.
The Patriot's organisation has also been accused of spying on rival teams in 2007.
The National Football League (NFL) has said it will investigate claims that Pittsburgh Steelers staff were unable use their headsets in a game against the New England Patriots.