Swindon then enjoyed their best spell, but Oldham took all three points when Danny Philliskirk dived to head home a left-wing cross from Jonathan Grounds with 13 minutes remaining.
The defeat was a second in a week for Cooper's men after they lost their unbeaten home record to Walsall.
"We didn't perform in our last game but we deserved to take something from this one," said Cooper.
"We had our chances, but if you don't take them you are always liable to concede at the other end.
"The first half was a non-event. We didn't start particularly well and it was all a bit flat.
"We are trying to play football but at times you have to find the space otherwise your passing will break down.
"Oldham went in front with a freak goal but in the second half we started much better and got ourselves back into it.
"At 1-1 I thought we would go on and win the game, but we missed our chances and didn't defend properly from a cross into our box."