Manager Paul Dickov was delighted with Oldham's superb second-half comeback which saw them win 3-2 after being 2-0 down at the break.
A Richard Cresswell own goal started the revival after the home side led through goals from Matt Lowton and Ched Evans.
Lowton was sent off following a second booking before Kieran Lee equalised and Shefki Kuqi scored a stoppage-time winner from the penalty spot.
Harry Maguire, who hauled down Reuben Reid for the penalty, was also shown a red card and Dickov said: "It was fantastic. When you're 2-0 down at half-time, especially at a place like this, you tend to think the worst.
"But I didn't think there was a lot in the first half. Two individual errors cost us and when you make silly mistakes defensively against a team as good as Sheffield United, you're going to get punished.
"I thought, attacking wise, we caused them problems in the first half and we just asked the boys to believe.
"We knew how important the next goal was. As well as the boys having a really good go and showing desire, I thought we played some really good, attacking football."
Sheffield United boss Danny Wilson blasted his side for not seeing out the game.
He said: "We had enough of the game in the first 45 minutes to put the game to bed. We've overplayed and had an extra pass at times. We haven't finished off the good work and it's basically cost us later in the game.
"We had enough chances in the second half as well before they scored. That's a big lesson for us. If you don't do your jobs properly, that's the price you pay."