The Lowland League side had already written themselves into the record books by making it through to the third round for the first time in the club's 113-year history, however, Saturday's encounter against Peterhead at Christie Gilles Park proved a bridge too far.
The League One side’s 3-0 victory could have been far less comfortable had Strollers scored when they were on top in the first 20 minutes.
The game then swung in the favour of Jim McInally's men when Balde was sent off for a late challenge in the 28th minute.
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"The sending off played into Peterhead's hands and it was always going to be hard with ten men after that,” said Jardine.
“There was no malice in the tackle so it's one of those ones where 50 per cent of referees will give a yellow card and the other 50 it will be red.”
The visitors failed to capitalise on their numerical advantage as Scott Brown saw his penalty saved by Strollers No 1 Macallan Whyte two minutes before the interval.
However, Russell McLean did convert from 12 yards ten minutes after the restart to give Peterhead the lead before Brown made amends for his first-half penalty miss with a deflected effort that flew past Whyte.
Lyall Cameron added a third in stoppage time from close range.
And while admitting it always going to be a difficult ask to keep that level of intensity up for 90 minutes, Jardine thought a shock was on the cards in that opening period.
"We got the ball forward and put them under pressure early on and I thought it was only a matter of time before we scored," he said.
"Peterhead are a decent side with some right good players and are led by a top manager.
“It was just a couple of sloppy goals we conceded, but the players can be proud of what they put in on Saturday.
“But now it's time to get back to the bread and butter of the league because we want to try and close that gap at the top."