After he allowed five runs to the Cardinals through the first three innings, a tunnel camera showed Strasburg rubbing an area between his neck and right shoulder.
"Quite honestly, that shot shouldn't have been shown, so I'm a little perturbed about that," Martinez said, according to MLB.com's Mark Feinsand. "It shouldn't be there. Honestly, that camera, there are rules and regulations about that. It's not supposed to go down in the tunnel. It's in black and white."
Strasburg, whose velocity has been around two miles per hour slower this season than during his last full campaign in 2019, returned to face eight more hitters after the camera caught him rubbing the area.
The righty escaped a bases-loaded jam in the fourth, but he was yanked in the fifth after three runners reached base. The 32-year-old gave up eight runs (seven earned) and five walks during a 14-3 loss.
Martinez said Strasburg, who has experienced shoulder issues in the past, didn't mention feeling any problems during the outing.
The veteran, who instead chalked up the bad night to throwing a lot of poor pitches, called a camera showing him in the tunnel a "joke."
"There's got to be some sort of safe place in the stadium," Strasburg said. "There have been plenty of other starts where something is not feeling right, and whether you treat yourself or you have a trainer come treat you, it's just part of the business.
"I went out there and I gave it everything I had; it wasn't good enough tonight. There should be some sort of privacy. People don't watch the games on TV to watch some sort of spy camera watching what the player is doing in the tunnel."