Peterson confirmed that he found out two months ago that he was the father of the 2-year-old boy, who died last Friday from injuries sustained in an alleged aggravated assault.
Peterson said he had been supporting the boy's mother financially and had been in contact with her to make plans to meet his son.
"I was planning on seeing him," Peterson said. "I had a talk with his mom, and we got some things together as far as financially helping her.
"Unfortunately, this situation took place. It's devastating. A lot of people won't ever understand the situation that I'm in and see it the way I'm seeing the situation. It's tough, but I'm able to deal with that and got a good supporting cast around me that's been supporting me through this tough time."
The boy's mother was in a relationship with Joseph Patterson, who was arrested on charges of aggravated assault and is being held on $750,000 bail. Lincoln County attorney Tom Wollman said Tuesday he could ask a grand jury to consider additional charges in light of the boy's death.
Peterson rushed for 62 yards on 10 carries in Sunday's 35-10 loss to the Carolina Panthers, just two days after the death of his son.
"It was tough, don't get me wrong," Peterson said during an "E:60" interview that will air in its entirety Tuesday at 7 p.m. ET. "Don't get me wrong, it was tough. But, you know, I just prayed. I just prayed to give me the strength to get through, and I was able to get through. The league is a fraternity, and we support each other."
Peterson said he does not expect to return to South Dakota to be involved with the police investigation.
"I have the contacts that I need to be able to stay involved," he said.
Peterson said he has not paid much attention to tabloid reports about how many children he has, adding, "People are going to speculate. They're going to say this and that.
"I can't let that bother me. I've been too focused on trying to mourn and be there for his mother and take in the loss of my son. I haven't been able to focus on anything else outside of that."