Crewe have still managed only one league win this season, but at Boundary Park they produced a solid all-round display that was capped by Oliver Turton's first senior goal.
Turton, a 20-year-old academy product, gave Crewe a first-half lead, only for Oldham to rally and Charlie MacDonald denied the visitors victory.
Johnson said: "This is a good point, considering that we conceded the first goal and had to show character to come back into the game.
"We've stopped the rot, which is important. We needed to get at least one point on the board and now we can go into our next game and build on that.
"We started well and had a couple of chances without really working their keeper.
"But then we started giving the ball away ridiculously, which meant all the momentum went the other way.
"Crewe were causing us problems with their movement, so I changed things tactically at half-time to give us a better shape.
"We'd had three or four players whose decision making wasn't up to the usual standard and you will always struggle when that happens, no matter what level you are playing at.
"But we improved after half-time and had most of the territory, so it's a shame we couldn't find a winner."
Oldham's James Dayton forced a save from Steve Phillips - making the 600th appearance of his career - but Crewe grabbed the lead after 13 minutes when Turton took aim from just outside the box and saw his low drive spear home.
The visitors almost made it a quickfire double, with Oxley tipping away Max Clayton's deflected effort before Byron Moore headed the rebound inches over.
Oldham also went desperately close after 18 minutes as Sidney Schmeltz crossed from the right and MacDonald slammed his eight-yard shot against the post.
Phillips rescued Crewe in the 35th minute, saving with his legs after Adam Rooney burst on to Dayton's through-ball.
But Oldham pulled level nine minutes after the break as Dayton hooked a pass over the Alex defence and MacDonald converted with a stretching six-yard volley.
- Sports & Recreation
- Oliver Turton
- Charlie MacDonald