Johnson was joined by general manager Mike Rizzo and pitching coach Steve McCatty.
Strasburg, who is 15-6 with a 2.94 ERA and leads the National League with 195 strikeouts, had Tommy John surgery to replace an elbow ligament two years ago.
"I'm not sure any of us understand," Johnson said. "But it's the right thing to do."
For months, Johnson has been peppered with questions about the Nationals' plan and he always said the team would limit his innings. Strasburg has thrown 156 1/3. He's averaged just under six innings in his 27 starts.
"I've listened to all the gurus. I've had all the advice. None of it made much sense," Johnson said.
Strasburg is projected to make his final two starts on Friday against Miami and on Sept. 12 in New York.
"It's no secret that Stras is an intense competitor, that he wants to be here, wants to be contributing, wants to be helping and I'm sure it's probably eating him up more than anybody involved in this whole thing because he wants to be here and helping his teammates. He's worked harder than anybody coming back from that surgery, and this what you dream about being a part of. I know how he feels," Johnson said.
The Nationals entered Monday with the best record in the majors and leading the NL East by 6½ games over Atlanta.
"I don't look at this as the only chance you're going to get to be in the postseason, the World Series. This team wasn't just piecemealed together for one year. It was built to last, and we're trying to make sure it lasts," Johnson said.