Swindon boss Kevin MacDonald witnessed another game that got away as his side failed to end a dismal run of home failures.
But it could have been worse for the hosts, who went behind when 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.
MacDonald said: "We created a lot of chances but did not score from them.
"If we play like that over the remainder of the season we will win more than we lose but it is getting tight now at the top.
"We lacked any kind of conviction and care in front of goal and that is why we only have one point instead of three.
"Adam Rooney's goal was a terrific finish coming just after we had conceded, but you score as a team and concede as a team and we did not convert our chances."