The Englishman spoke in reference to that tie specifically, but it seemed also that he was making a nod to the decision of city rivals Hearts to dilute their first-team squad in a cup match with Livingston last week.
The Tynecastle side that night was made up of a number of callow young players and were beaten into submission and a 4-1 defeat. It was an unfamiliar starting line-up and an unfamiliar result for a team which is at the top of the SPFL Championship table. Celtic also lost at the weekend having made 10 changes to their side.
There was method to that, of course, since the Scottish champions had a crucial Champions League tie with Maribor to prepare for. The idea of flooding his team with youngsters seems just as foreign to Stubbs as a midweek venture into Europe and he believes that he owes it to Hibs fans to always select his strongest team.
"I don't believe in making wholesale changes, I don't think it's right; I don't think it's right to the paying public," said the Hibs head coach. "I think they deserve to see a team on the pitch that is worthy of winning the game. I'll never put a team out with eight kids and one or people that are on the fringes of playing.
"From my point of view, I don't think it's right for your fans to turn up when they've paid hard-earned money to see that. One thing I wouldn't do is put a weakened team out to paying customers that are coming to see the team and suddenly you have names that they don't recognise.
"I'm trying to get in the mind-set and philosophy that you approach every game to win every game. We could potentially win this competition so why would I want to take chances in the early rounds, or any round, to put a team out that might not necessarily be one that could win the game?"
Hibs fans will certainly recognise the name Danny Handling tonight. The 20-year-old scribbled it on a new four-year contract last night too, a deal which is intended to tie him to the Easter Road club until at least 2018. The forward had always been keen to extend his stay at the club, so much so that he has waited patiently for six months to complete the deal.
"It has been a long process and I am delighted it is over the line," said Handling. "The contract talks had been going on since the Raith Rovers Scottish Cup game last season. It was a big worry because the old manager [Terry Butcher] offered me the contract and then he got sacked and Alan Stubbs came in.
"I did wonder if anything was going to be on the table, especially when I saw the likes of Jason Cummings sign his deal. I thought at one point: 'What about my contract, why is my deal taking so long to be concluded?' Luckily enough the new manager liked me and offered me the same contract."
Ian Murray wants only to give the young forward a cup defeat tonight, the Dumbarton manager returning to the club where he made his start as a player. "We would try to use the crowd against any bigger team that we play, whether that be Hearts, Rangers or Hibs because they're all the same," said Murray, who is without Lee Mair tonight.
"The Hibs supporters expect to win every game, they expect to beat the full-time teams never mind the part-time ones. But it is a one-off in terms of having to win or you are out and if we are to do that we need to defend better than we have been doing."