Kelly's men were eliminated from the cup by Medda in a weekend replay and the long-serving gaffer said: "We heard a lot of talk about in-fighting and unhappy players before we played them, but clearly things are not as bad as some people have made out
"We certainly found no signs of any disharmony in their camp in either of our two games.
"If anything, there was a great togetherness and spirit about their team, so I wouldn't be in the least bit surprised if they went a long way in the Scottish."
His comments will doubtless strike a chord with Medda counterpart Chris Strain, who has long since insisted he and his players would silence their critics.
He said: "All the whispers about players wanting out the door were put to bed by the hunger and determination on show in the two games against Shettleston.
"I felt the guys rolled up the sleeves to battle their corner in what were really difficult circumstances and I was delighted with their reaction, not least because we'll need plenty more of that same character to get past Cumnock.
"I haven't seen a lot of them this season but what I do know is they have top-quality midfielders in the likes of Willie Howie, John Johnston and the ex-Kilbirnie Ladeside playmaker Paul McInnes.
"Being an Ayrshire derby makes it even more of cup cracker, however we must focus first and foremost on our own performance as a winning result could really lift our season."
One of the Meadow Park success stories to date, full-back Robert Halliday, believes he and his team-mates must concentrate on their own playing strength rather than Cumnock's.
HE SAID: "Cumnock will come here feeling confident about getting a result, but there are few better teams than Irvine Meadow when it comes to creative, attacking football, so we must avoid being dragged into a war of attrition like we did against Shettleston.
"Liam McGuinness is getting back to his best as is Richie Barr, whose work-rate is phenomenal, while the return to training in recent weeks by Adam Strachan has given everyone connected with the club a massive boost.
"He is one of those special talents capable of winning games with a touch of genius and I'm pretty sure the Cumnock defenders will not fancy the prospect of him running at them.
"He was only introduced for the last five minutes at Shettleston on his first game back and is lacking match practice, but whether from the start or coming off the bench I can see him having a big say in this week's cup-tie.
"It's a massive game but we have prepared well by winning 3-0 against a youthful Clyde side on Monday night and the plan is to train tonight and get ourselves in the best possible shape for facing Cumnock."