Martinez, a right-hander trying to win a job in the starting rotation, and the Cardinals express regret over the lewd postings that have since been taken down.
"There was a confusion," Martinez told ESPNdeportes.com on Wednesday. "It's my Twitter account and I understand what people are talking about and I should be responsible, but I want you to know that I do not have time to be doing that kind of thing.
"I talked to my teammates, the manager, the general manager. Everybody understood that I was a victim. My agent helped me and everyone was aware that I did nothing wrong. One must be aware that there are people out there willing to hurt me."
The Cardinals have no plans for disciplinary action against Martinez.
"I'm fighting for a spot in the starting rotation and that's what matters to me now," he told ESPNdeportes.com. "I don't have time to be on social networks doing bad things. These are problems that come to us and must be resolved quickly. From now on, I won't directly operate my account, I'll put a person in charge."
Cardinals manager Mike Matheny addressed the situation with Martinez and said the young pitcher accepted responsibility for his actions.
"We're embarrassed and he's embarrassed," Matheny said, according to the St. Louis Post-Dispatch. "I'm not trying to shove my morality down anybody's throat. I've made that very clear. But I also need to be concerned about it ... Realize, is this something you'd want your kids to see? Is this something that you want to be known for? Is this how you want to be remembered?
"We are, like it or not, role models. Regardless of your moral compass and where it points, those sorts of things that we're talking about are not things we want our kids seeing."
Matheny took the opportunity to speak with the players about social media.
"It heightens our urgency to make sure that we're diligent and we're disciplined to educate and to make aware that when something like this happens, it's going to be an embarrassment to you and when something like this happens, it's going to be an embarrassment to us," Matheny said, according to MLB.com.