Latics' 2-2 New Year's Day draw with top team Notts County was seen as a drastically improved performance by David Unsworth's men compared to the Boxing Day fixture.
But Notts County head coach Williams said he did not see too many differences in how Oldham approached the second meeting between the sides in less than a week, with the Magpies winning the first 4-1.
Instead, he felt it was the flaws in his own side's game on the day that were significant in twice surrendering a second half lead second time around.
"We knew they have very good players in the team and I think they're probably at the beginning of a process of rebuilding and having some pride back in and they're at the beginning of that." said Williams.
"I think they performed in actually a similar way to how they did at Meadow Lane. When we made the breakthrough was a really key moment for us but we needed to then control the game and try to be able to build up calmly and then we don't need to score again. But of course we conceded very soon afterwards.
"I think the two games were similar in many ways but we let the game slip out of our grasp.
"We struggled with transition later on in the game. It's a very, very big pitch and I think we began to look a bit off the pace in the transitions and we were allowing too much territory to be gained for Oldham. We are normally better at trying to stem the flow of the attack earlier on but we didn't do that well enough and we allowed them to take territory, and then there were a lot of set pieces for us to defend and that cost us in the end.
"We created good openings but I think the game got away from us in the transition. Oldham were brave and left guys at the top of the pitch to try to counter attack off when they defended deep, and that worked well for them.
"When you go in front twice it's really frustrating to not see the game out."
Nathan Sheron scored Latics' first equaliser three minutes after Macauley Langstaff broke the deadlock with his 22nd goal of the season, capitalising on a mistake by goalkeeper Sam Slocombe who came out of his area and gave Sheron an open goal to aim for.
"The first goal was unfortunate because it's kind of a routine cover-up for us," Williams explained. "The goalkeeper is always in a great position to mop up behind the line and did that in a routine way but there was a problem and we didn't clear the ball correctly. It's very disappointing but I don't want to be so harsh on the guys, particularly Sam because he's really been incredible to help us to control games.
"It happens and it's disappointing."
Joe Nuttall scored his second goal in as many games - both against Notts County - via the penalty spot after a foul on Peter Clarke which Williams felt was dubious.
"There was so much holding in both boxes, I find it very odd it's a fact that we're in the opposition box more than any other team in the league, we put more crosses in than any other team in the league, players are being held and pushed on the floor and grabbed, it's normal, but we don't seem to get too many penalties our way.
"It's disappointing because there's a lot of holding in both boxes constantly."
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