Chiefs salvaged a point against Sundowns in a 1-1 draw after Phathutshedzo Nange cancelled out Aubrey Modiba's opener early in the second stanza.
Amakhosi had a big chance to snatch all the three points late in the game from the penalty spot but Keagan Dolly's spot-kick was saved by goalkeeper Reyaad Pieterse.
"I think we started very well, first 20 minutes we were the better team first-half, we had about three break attacks we didn't take one," Zwane said after the game on SuperSport TV.
"From there we dropped a little bit and allowed them to control the game in the middle and in the last six, seven minutes of the first half we were back in the game, we showed glimpses.
"Creating goal-scoring opportunities but not clinical. At halftime, we told them that they should be aware of the diagonal passes, of which we conceded from there.
"From there were dropped and allowed them to control the game but look, it was given for them, for the fact that they had nothing to lose.
"They came here knowing very well that whether they lose or win the game they've got nothing to lose and when you're playing against an opposition who are not going to push you to that extent you become vulnerable because they are more relaxed and you're tense, you're chasing the game.
"I think just after conceding the goal we now had to make changes, take the game to them, make sure that we get the equaliser.
"We managed to get the equaliser from a great movement, good passing game from the boys of which we expect that to happen consistently.
"But we're playing in patches like I said, we're afraid of losing the ball but it's something we're going to work on. Just one extra day of preparing the team much better compared to when we were playing back-to-back and we did not have enough time to prepare the team in terms of sessions."