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Latics beat Wednesday 2-1 after extra time on Sunday (November 8) thanks to Will Sutton's header.
Now, in a clip which has been widely shared on social media, Rothwell praised the Oldham fans and stated who he wants the club to draw in the Second Round.
In an interview with broadcaster TNT Sports after the match, Rothwell said: "Fantastic - did you see our suporters tonight? Weren't they rocking?
"And when we sung 'Stand up if you love Oldham', everybody in the stadium stood up.
"Everybody here loves Oldham just like I do, I'm passionate about Oldham."
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Rothwell was stood amongst the supporters throughout the match, saying: "That's where I go, I've got to support the lads and make sure they keep banging that drum. Oh yes."
When it was suggested that a "cup run would help", Rothwell agreed before making no secrets about who he wants to face next in the cup.
"We want Rochdale, here," Rothwell said.
"Not at Rochdale because they can only take a half dozen of our lot, we can take all of Rochdale's here and they can all come here and we can have a really good cup run, giving them a good spanking."
Oldham will find out their next opponents in the FA Cup when the Second Round draw takes place at 6.45pm tonight (Monday, November 9) which can be watched live on TNT Sports, HBO Max, and the TNT Sports YouTube channel.