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GALLERY: Past weekend's sporting pictures
The Dube Birds, who thrashed Black Leopards 5-2 last Friday, trail their Soweto neighbours by two points with two games left in the season.
"I don't think there's any pressure on us at the moment," Chabangu told the league's website.
"We are not the one on top of the log at the moment. The pressure is on the team above us because they have to make sure that they keep winning, because if they don't, we will do our job and results will follow."
Reflecting on Swallows' recent victory, Chabangu felt his team did well to sink relegation-threatened Leopards on their own turf.
"I think we felt a bit of that (pressure) in Giyani, because everyone knows that this is not an easy place to come and collect points but we did," he said.
"That's something that isn't easy to deal with knowing you're supposed to win and not only win, but win convincingly, because goal difference might come into play at the end.
"We like the spot we're in and we're just going to keep working," concluded the former Mamelodi Sundowns man.
Swallows will enter their campaign with games against Platinum Stars (home) and Maritzburg United (away), while champions Bucs face Bloemfontein Celtic (home) and Golden Arrows (away) in their final two fixtures.
