Peter Shalulile scored the only goal of the game at Loftus Versfeld with 54 minutes on the clock.
The result handed the Brazilians a narrow advantage ahead of next week's return leg on Tuesday.
Reflecting on the result, Kanzari explained that there was little to separate the two sides.
He said on SABC Sport: "It was a very tactical game and both teams they were no kind of clear-cut occasion either for Sundowns or for Esperance.
"But you know, at some point there was like lack of concentration and they score a goal.
“But I hope that in the second leg we do the job and get through.”
Mamelodi Sundowns striker Peter Shalulile has hailed head coach Miguel Cardoso's tactical approach following their crucial 1-0 victory over Esperance in the first leg of the CAF Champions League quarterfinals at Loftus Versfeld on Tuesday.
Mamelodi Sundowns have expressed their sadness at the violence that erupted during their CAF Champions League encounter with Esperance at Loftus Versfeld Stadium on Tuesday.
Mamelodi Sundowns coach Miguel Cardoso admits his side struggled to stick to their game plan against Esperance in the CAF Champions League on Tuesday.
Mamelodi Sundowns took a crucial step towards the CAF Champions League semi-finals with a 1-0 victory over Esperance in their quarter-final first leg at Loftus Versfeld on Tuesday afternoon.
