The League One side dumped Nottingham Forest, from the Championship, out of the competition to leave Dickov's fellow Scot Alex McLeish still looking for his first win since taking charge at The City Ground.
Now Dickov wants Oldham to be drawn against Premier League champions Manchester City, his old club. Dickov said: "With my Manchester City connections it would be nice to meet them in the next round. Financially it would mean a lot to the club and it would be great for me on a personal level.
"If we can make some money in the next round, you never know - the chairman might let me bring one or two players in as well. But for the time being we just want to enjoy today's game because I am very proud of my players for the way they come back into this game after losing an early goal.
"To be honest I thought we were guilty of showing Forest too much respect in the first half but I said to them at half-time, `It's the FA Cup and if you are going to go out, don't go out with a whimper'.
"I thought we were excellent in the second half, played some great football and thoroughly deserved it. We showed great desire and got the rewards for it."
Oldham had to bounce back from the loss of a 13th-minute goal when striker Matt Smith turned an Andy Reid free-kick into his own net.
But Robbie Simpson struck twice within four second-half minutes to turn the game in the visitors' favour. He equalised in the 54th minute with a 25-yard shot that crept inside Lee Camp's left-hand post and four minutes later produced a looping header to convert a superb cross by Dean Furman.
Forest skipper Danny Collins was sent off in the 60th minute for bringing down Smith, and the home side were punished further when leading scorer Jose Baxter whipped in the free-kick to give Oldham a two-goal cushion.
Substitute Billy Sharp pulled one back in added time with a left-footed finish inside the box but it was too late.
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- Premier League