Stellies are currently in third position on the log, but any slip up might open the door for fourth-placed Sekhukhune United to leapfrog them.
Barker says the precarious position his opponents find themselves in makes their job all the more harder.
"When the fixture list came out right at the beginning of the season, seeing we're playing City on the last day – I always anticipated that it would be a great way to end the season," said Barker.
"A massive derby between the two clubs, and as it panned out over this season, it's a very key game for both clubs, obviously for different reasons.
"Obviously, I think they're fighting for their lives and therefore it doesn't make the game any easier at all, and in fact I believe it makes it [more] difficult because they'll be fighting for survival and it does become tricky."
Having been edged out by Tanzania’s Simba SC in the Confed Cup semi-finals, Barker says next season they have to continue where they left off after experiencing the thrill of continental football.
"It's important that we also focus on what we need to achieved and keep our commitment as high as it can be until the last kick of the ball," he added.
"So we've prepared well, we want to win derbies and we also want to be finishing in that third position to go the [CAF Confederation Cup] again."