Former Manchester United players Gary Neville and Roy Keane were both highly critical of Martinelli on Sky Sports, with Neville saying his actions were "absolutely disgraceful" and describing the Arsenal winger as an "idiot".
"I really didn't understand he was seriously injured in the heat of the moment," Martinelli posted on Instagram.
"I want to say I'm deeply sorry for reacting. Sending Conor all my best again for a quick recovery."
Since Trent Alexander-Arnold left for Real Madrid in the summer, Bradley has been Liverpool's first choice right-back, starting 12 of their Premier League games this season.
Manager Arne Slot's potential alternatives are limited with Joe Gomez as an option, while Dominik Szoboszlai has also slotted in as a full-back on occasion.
The more likely option is Jeremie Frimpong, who has been performing further forward down the right flank in recent weeks.