The Iron had to come from behind to win 2-1 at Glanford Park thanks to second-half goals from Jonathan Forte and Martyn Wooford.
Djeny Dembo had put the League One side ahead in the first-half as the Iron struggled to impose themselves against lower league opposition.
Jonathan Forte continued his new lease of life with the equalising goal after 65 minutes, and winger Martyn Woolford got a winner with seven minutes to go.
"Forte was yet again exceptional. It was a great goal that he scored and I was really pleased that Woolford scored a goal too," said Adkins.
"We weren't happy with the performance level, and we know that. We'll analyse it though and try to keep improving, and developing on that. We knew it would be a very challenging evening against an Oldham side who pass the ball well.
"We tried to play an expansive game with two wingers but I felt we struggled in the middle of the park at times, but we changed the formation in the second half and it worked."
Adkins also confirmed his intention to fine midfielder Sam Togwell, after he was sent off for two yellow cards despite only entering the match as a substitute. He will be suspended for Saturday's Championship game against Norwich City.
"It was an avoidable booking for us and we're disappointed he won't be available at the weekend," he added.
"Sam made it an easy decision for the referee - who I felt made some very interesting decisions - but at the end of the day Sam's going to be light in his pocket because he'll get fined, and get fined heavily for that."