The US space agency said that ruling out defects "does not necessarily mean the hole was created intentionally or with mal-intent".
Drew Feustel needs to return to Earth this week after his stay on the global space station, but he did it as a parting gift.
The Soyuz MS-09/55S capsule - the vehicle at the center of a growing controversy over an unexpected and unexplained hole which appeared in its hull - remains attached to the International Space Station.
He also wrote "spasibo" (thank you) and signed his name on the craft in chalk.
Both Feustel and Arnold participated in dozens of educational downlink events while in space, as part of NASA's Year of Education on Station, reaching more than 2 lakh students in 29 states, the statement said.More news: White House tells FBI it can talk to anyone about Kavanaugh
Rogozin, according to news reports last month, initially refused to rule out the possibility that an astronaut, not a worker on the ground, might have drilled the hole.
That suggests the hole was "an isolated issue", NASA said, not one expected to reappear on the next Soyuz, which is scheduled to launch October 11 from Kazakhstan with NASA's Nick Hague and cosmonaut Alexey Ovchinin.
After the hole was found, Rogozin and NASA Administrator spoke over the phone on September 12 about the leak.
NASA Administrator Jim Bridenstine plans to meet Rogozin - their first in-person encounter-when he attends the launch.
This is Gerst's second stay aboard the space station and his first command.
The trio returning from the ISS to the Earth are Roscosmos cosmonaut Oleg Artemyev and NASA astronauts Richard Arnold and Andrew Feustel. NASA says it hopes to sort the problem out then.