Phili joined Amakhosi from Stellenbosch earlier this week and was introduced in the second half as Chiefs' return to the MTN8 ended at the first hurdle.
Golden Arrows secured a place in the semi-finals after Khulekani Shezi scored shortly after the interval to hand Abafana Besthende a 1-0 victory.
Despite the disappointing result, Da Cruz believes Phili's integration into the team should be handled gradually as the youngster adjusts to his new surroundings and the coach's tactical demands.
"They are coming into the team step-by-step," Da Cruz told SuperSport TV.
"Phili needs to work physically again a little bit and to understand also our modern game, but they will come step-by-step."
The French coach has already stressed the importance of giving his new arrivals enough time to settle, and Phili's debut provided his first taste of competitive action in Chiefs colours.
Da Cruz will now hope to see the youngster make further progress as Chiefs turn their attention to the Betway Premiership.
The coach was also disappointed with Chiefs' inability to convert their opportunities against Arrows, insisting that the team created enough chances to change the outcome.
"The mindset, the comfort of the player, nothing to say because we missed a lot of chances today," Da Cruz said.
"The score is unfortunately the only one goal changes in the half and after that we tried to come back, but we had a lack of efficiency there."
Da Cruz also refused to blame captain and goalkeeper Brandon Petersen for the goal, insisting that the defeat was a collective responsibility.
"I don't want to say we lost because of one player," he added.
Chiefs must quickly regroup, with Sekhukhune United awaiting them in the Betway Premiership on Wednesday where they will be looking to make it two wins in a row in the league after beating Kruger United 3-1 in their opening fixture.
