Penney was caught on microphone making an obscene comment about the journalist, who had grilled him on Wednesday about the Crusaders' poor form and asked him if he would still be in charge next season.
After the end of the tetchy press conference in Christchurch on Wednesday, Penney told a member of the club's media staff that the New Zealand journalist was "a disgrace" before using an obscenity.
"A private comment to a colleague was inadvertently recorded on third-party microphones, and Rob has since apologised to me for what was said," Crusaders chief executive Colin Mansbridge said in a statement.
"I spoke to the reporter today and he has accepted our apology," Mansbridge added.
The Crusaders won the title in each of the previous seven years under Penney's predecessor, new All Blacks head coach Scott Robertson.
But they have lost 10 out of their 12 matches in this campaign.
Defeat at home to the table-topping Auckland Blues on Saturday would end their wafer-thin hopes of finishing in the top eight that make the playoffs.
Penny, 60, formerly coached in Ireland with Munster and also in Australia at NSW Waratahs, where he was sacked after losing his first five games in 2021.
