The draw, which was held in Johannesburg, saw Sundowns drawn alongside Algerian side MC Alger, where Mokwena is currently at the helm, in Group C.
The two teams are joined by Al Hilal of Sudan and DR Congo’s St Eloi Lupopo, who eliminated Orlando Pirates in the preliminary stage, and Zwane shared his thoughts on the outcome of the draw.
"An interesting group, and that's the Champions League for you – you don't get to choose who to play, but for us as Sundowns, I think we're comfortable with the group," said Zwane.
"I think we have a good team, with good players who can get the job done. We just have to bring our A-game to each and every game that we're going to play so that we can qualify for the next round."
Pressed for his thoughts on coming up against Mokwena, who he worked extensively with as both an assistant coach en route to Sundowns' maiden continental crown in 2016 to head coach in more recent seasons, Zwane acknowledged his former mentor's role.
"To be honest, he's a good coach and he's a good human being. Working with him was very exciting because we got to learn a lot as players," he added.
"We got to improve a lot as players, so for me, I really appreciate the time that I spent with him."
The opening two rounds of the group stage is set for 21-30 November, with the final round scheduled for 13-15 February due to the two-month recess necessitated by the Africa Cup of Nations in December and January.