Amakhosi, who are sixth on the PSL table, recently snapped a four-game losing streak with a 2-0 win over the title-chasing Brazilians.
And although the Urban Warriors are 12 points poorer than Downs, Khumalo is naturally wary of allowing complacency to creep in.
"It is very important that we remain focused on the job at hand," he told his club's website.
"It was important that we turn the corner against Mamelodi Sundowns on Wednesday but now that is water under the bridge.
"Ajax Cape Town will be even tougher than Sundowns was as they also have not been doing well in the past couple of games.
"We will need to be at our best to beat them. We cannot rest in our laurels just because we have won one game. We have not arrived yet," concluded the Glamour Boys legend.