According to court documents, campus police called to the on-campus housing complex to break up a party the night of the Blue-White scrimmage on April 25 discovered "marijuana residue" and related items in the apartment.
Hearing a fire alarm, police knocked on a door, but no one answered, authorities said. A woman with a key unlocked the door from the outside, and officers saw and smelled the drug, they said.
Police said Tuesday they were investigating. No charges have been filed.
Reports about the investigation have been broadcast on television and published in newspapers around Pennsylvania.
"That's been blown way out of proportion," Paterno said at a function with more than 400 Penn State alumni and boosters in the Washington, D.C., area. "It's a party, and my guys horsing around with marijuana? You know, we test them all the time. And the four kids who were renting the apartment were not in the apartment when the police got in there."
Paterno said that he plans to learn more details this week and that university judicial officials will probably do their own investigation.
"But they're four young kids. They're sophomores in college, and who knows?" Paterno said. "Unfortunately a lot of times your buddies come up for the Blue-White game. I'm very reluctant to take any kind of position. If I find out somebody was dead wrong and really involved in the whole deal, then we'll take appropriate action, but right now I don't think we would."
Paterno also said he was planning to meet Wednesday with linebacker Navorro Bowman, who sat out the spring scrimmage after getting into more legal trouble. A judge ruled last month that Bowman, the Nittany Lions' top tackler last season, violated his probation when he admitted, during a meeting with a probation officer, smoking marijuana in the offseason.
Bowman, from the Washington suburb of District Heights, Md., had been on probation after pleading guilty in May 2008 to disorderly conduct in connection with a campus fight. He has said he's "trying to stay above board, stay out of trouble."
Paterno said Bowman, 20, "just didn't do what he was supposed to do."
"He got in a little jam, and they told him he had to do some community work, and he didn't do it," Paterno said. "But he's had a lot of problems."
Asked if Bowman will play this fall, Paterno said: "If he does what he's supposed to do. ... If he does it, we'll go from there."
During the half-hour interview with reporters, Paterno reiterated many of his previous stands on a variety of issues. The 82-year-old coach would like to see a playoff system replace the Bowl Championship Series, he'd like the Big Ten to add another team and have a championship game and he plans to coach "hopefully three or four more years."
Paterno was asked about the idea of appointing a coach in waiting, as nearby Maryland has done with Ralph Friedgen. The university announced in February that assistant head coach James Franklin will be Friedgen's successor.
"I don't particularly like that idea," Paterno said. "I think what you ought to do is when the head coach is ready to go, you go. I don't think you have to bring in a guy in waiting because there's so many good coaches out there, and things change."