"I made a poor decision. I got caught in something that wasn't really my personality or me," Simpson told the newspaper.
The former Cincinnati Bengals wideout pleaded guilty to a charge of prohibited acts involving controlled substances in March after police found several pounds of marijuana in his Kentucky home. He was sentenced to 15 days in jail and suspended by the NFL for the first three games of the season.
"Everybody makes mistakes," Simpson added. "I just want people to kind of forgive me."
Simpson, who was a free agent, signed with the Vikings in April.
Simpson had a more serious drug trafficking charge dropped after he said the marijuana was only meant for him and his friends.
"I'm not a drug dealer or anything," Simpson said. "I'm not out there like that. I just made a poor decision. I paid my debt to society. I want to help people not make the same decision I made. One of my goals is to help people not go down that path like I did."
The 2008 second-round pick of the Bengals is coming off his best NFL season, with 50 catches for 725 yards and four touchdowns.