The Latics were 2-0 behind at half-time but were transformed by a treble substitution at the break, but Matt Smith and Bobby Reid were both denied by superb saves.
The home side's only consolation came after 73 minutes as Korey Smith was brought down by Jordan Mustoe, allowing Baxter to send Mark Gillespie the wrong way from the penalty spot.
Oldham remain in danger of relegation after suffering their first defeat in four matches under Johnson.
The recently-appointed Latics manager said: "The first half performance was nowhere near good enough and I apologise.
"I'll take the blame for this one because, in trying to get the lads ready for a big game, I might have overcooked them in training. They looked leggy, but you can still get results in those circumstances if you have the right mentality.
"In the first half there was a general laziness to make the extra yard or have the extra spark defensively or in attack.
"It's like we need a punch on the nose before we get going, so that needs to change.
"I can't repeat what I said at half-time but there were home truths and, to be fair, the lads reacted.
"We could have got at least a point because the second half was much better. But it couldn't have been much worse."