Amakhosi extended their winning streak to four games when they won 3-2 against Maritzburg.
Keagan Dolly's 5th-minute opener was followed by Christian Saile's 10th-minute goal.
However, a goal from Rafiq De Goede and an equaliser from Amadou Soukouna meant that the game went to halftime on a draw.
Then, Yusuf Maart's 76th-minute penalty secured a victory for Chiefs.
Zwane insists that he wasn't anxious because he believes in his players.
"I did not panic at all to be quite honest. Simply because I believe in our players, I believe that as soon as we take control of the game, we can create chances and be able to score. As long as we still have Christian (Saile) on the field, we have Ashley (Du Preez) on the field and Keagan (Dolly), Mdu (Shabalala), we can create goal-scoring opportunities and be dangerous," he said.
Ashley Du Preez did not start the season very well, which resulted in him being put under pressure by fans. Zwane says injuries made it hard for the striker to strive.
"We've always believed in Ash. Top player, top striker, very explosive, team player as well. Unfortunately for him, his progress was hampered by injuries. Whenever he came back and we thought he had regained his form, some niggling injuries will take him out for some time," he added.
Mangethe has blamed injuries for his teams' inconsistency this season.
"This season we've been unfortunate when it comes to having a consistent line-up. We came into this game, and we lost Siya (Siyabonga Ngezane), that for me could have done better for us. It's been a story of our season where we lose very key players, so that broke our momentum along the way. So, when you are building a team, you are going to have challenges that you are going to have to face," he concluded.