Alassane Diarra scored the only goal at the Levy Mwanawasa Stadium in the 76th minute to hand the Zambian Premier League side the advantage heading into next week's second leg.
Reflecting on the tie, Mbewe admits his side could have scored more goals against the Betway Premiership campaigners and is hopeful they can secure their progression to the knockout rounds with another strong performance in South Africa.
"Coming into this game, we knew it was not going to be an easy encounter, considering the experience and maturity Kaizer Chiefs have in this competition," Mbewe said on ZamFoot.
"I am happy with the way the boys fought and approached the game. Despite missing several chances, they showed great commitment and created numerous opportunities."
"Sometimes, that is the nature of football. You can create so many chances and end up scoring just one goal," added the head coach.
"However, we have to go back to training and continue improving. We need to be solid, remain compact and ensure that we do not give Kaizer Chiefs the space to dictate play.
“We are pleased with the result, but we know there are areas we need to work on as we prepare for the next match in South Africa.”
Durban City coach Eric Tinkler has challenged his players to improve their finishing after their 3-1 victory over AS Port Louis 2000 in the first leg of the CAF Confederation Cup second preliminary round on Sunday.
Kaizer Chiefs coach Fernando Da Cruz remains convinced that his side can turn their CAF Confederation Cup campaign around despite suffering a narrow defeat to Red Arrows.
Durban City took a major step towards the group stages of the CAF Confederation Cup with a Second qualifying round first leg 3-1 win over Mauritius side Port Louis on Sunday.
Kaizer Chiefs coach Fernando da Cruz is confident his side will overturn their 1-0 CAF Confederation Cup Second preliminary round deficit against Red Arrows.
