Davids has impressed with three wins in the last four matches since he replaced former coach Roger de Sa following his shocking resignation after just less than three months in charge.
United currently sitting seventh on the log table with 32 points from 25 matches, and next host log leaders Cape Town City on Monday before visiting title-contenders Bidvest Wits, top eight hopefuls Platinum Stars and PSL champions Mamelodi Sundowns.
However, Davids says his players will need to be at their best if they want to come away with something as he reflects on numerous mistakes made by his team in their recent match against Chippa United.
"We have to improve in those games because we've got top tier teams coming up and all three teams fighting for the title: Cape Town City, Wits, Platinum Stars in between, and then Sundowns," says Davids.
"So the next couple of games it's really out there to test us and we've got to improve things because normally you get punished.
"Against Chippa United, we really made it difficult for ourselves and next time you'll really not go away with three points.
"It was a fantastic first half and tactically we really put ourselves in positions where they didn't know what to do. But the disappointing things was that in the first half we should've sealed the game and not gone to the interval with a one goal lead."
Fortunately, against Erick Tinkler's side at the Harry Gwala stadium on Monday, Davids team will be boosted by the return of Evans Rusike, Brian Onyango and Deolin Mekoa after all three were suspended for the last match against Chippa.