Sharp was captain of Sheffield United last season when they took on Wrexham in the FA Cup in February, which they eventually won 3-1 after the first match went to a replay.
The striker became embroiled in a spat with Wrexham players and told them to 'shove that on your documentary' in a tunnel fracas.
He also vented at the apparent 'disrespect' shown by the Dragons, who were in the National League at the time.
Now Reynolds and McElhenney have hit out in the second season of Welcome to Wrexham, the documentary on Disney+.
"It was really interesting. It was psychology 101," Reynolds said. "It was like 'oh we own you right now'.
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"You're a Championship team, and second place in the Championship, you guys are amazing.
"And this guy we just got under his skin. It was so, so wonderful to see that we got under that guy's skin the way we did."
"We were living rent-free in that motherf*****'s brain," McElhenney added while giggling.
Wrexham managed to force Sheffield United to a replay after drawing 3-3 at the Racecourse Ground - with John Egan netting a 95th-minute equaliser for the visitors.
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The Blades won 3-1 at Bramall Lane, courtesy of two late goals in injury-time including one from Sharp, who has since signed for LA Galaxy.
Just weeks ago, the 37-year-old added further details about what happened during the FA Cup tie after he scored a hat-trick in a 4-3 win in the MLS.
"People don't even know the real story. Wrexham will put out what they want to on their documentary, and maybe I'll put out my own and tell them what really happened," he said.
"I scored the goal, which knocked them out, and a little scuffle happened in the changing room.
"I don't really like their manager anyway from past experiences, and he probably doesn't like me.
"It's just one of those things in football where it sometimes gets very overheated… I know what they're going to do; they're going to show the clips that make me look like a baddie.
"That's fine. I'll wait to see what happens and have my say afterwards. The record book says we beat them in the FA Cup, so they can have a documentary about it if they want."