The 24-year-old former Golden Arrows defender started both of Amakhosi's two opening games of the new season, against Stellenbosch and Polokwane City.
He was replaced by Paseko Mako after 75 minutes of the 1-0 win over Rise and Shine on Wednesday after going down with a knock but is expected to be fit for their upcoming encounter with Richards Bay on Tuesday.
Cross does, however, have competition for his place at left back, with Mako having joined the club following his exit from Orlando Pirates, while Nkanyiso Shinga was snapped up from Portuguese side FC Alverca.
Reflecting on the game, Cross said in the Citizen: "For me, having competition is good. You improve and you don't get complacent. So having guys in the same position helps me and is good for squad depth.
"I can take good things from them (Mako and Shinga) that they might have and I don't. And I might have things that they don't have."
Cross is in his second season with Amakhosi and hopes he can build on what was a difficult campaign last time out as the team ended in ninth place in head coach Nasreddine Nabi's first season in charge.
"It is normal to receive constructive criticism, it helps me as a player," the player added.
"It was a very difficult time but you have to go through those times, it makes you stronger as a person. I kept my head down and worked hard.
"Last season I think we got a bit excited after we started off (with two wins). But we have learned and we must take every game step-by-step, one at a time."