Swindon's inability to end a dismal run of home failures since mid-January saw them drop to fourth in the hotly-contested League One promotion race.
But Johnson's battling Oldham are still in the bottom four relegation zone despite coming close to snatching an unlikely win.
Lee Barnard, on loan from Southampton, put Oldham ahead in the 68th minute only for substitute Adam Rooney to equalise with a spectacular overhead kick three minutes later.
Johnson said: "I am pleased and angry at the same time. For 65 or 70 minutes we can compete with a top team but in the last 20 minutes we were not fit enough to sustain that level and keep our lead.
"Against a good team who are fit, that is what happens."
- Sports & Recreation