Wandile Duba opened the scoring in the 36th minute at the Peter Mokaba Stadium but the points were shared after Given Msimango netted an 81st minute own-goal.
The result saw Amakhosi return to eighth place with 30 points from 24 games, as Galaxy moved to third with 36 points from 25 matches.
Chiefs are averaging a goal a game this season and were guilty of a number of missed chances this time around as well.
Nabi told SuperSport: "It's true that as well as the opportunities we got was through our pressing, timing, it's what we worked on to prepare for this opponent, I'm tired of repeating myself on the chances we are missing.
"We should have scored more than one goal. We gave the opponents a chance to stay alive and we know they are good in set-pieces, and we tried to make changes, and we unfortunately conceded from a corner.
Chiefs were ultimately the masters of their own downfall as they conceding while trying to substitute an injured Inacio Miguel.
Nabi explained: "We didn't plan to bring on [Edmilson] Dove but when Miguel got injured, we had to summon him, we wanted to bring in George Matlou and Tashreeq Morris to bring height on set-pieces, the official wasn't fast enough when we wanted to change and we then conceded."
Stellenbosch FC face a daunting challenge as they travel to Cairo to take on Egyptian giants Zamalek in the second leg of the CAF Confederation Cup quarterfinals on Wednesday evening.
Chippa United coach Thabo September feels the Betway Premiership club will benefit from moving to East London.
TS Galaxy's dramatic transformation from relegation contenders to top-three hopefuls is gaining momentum, and head coach Adnan Beganovic believes his side is ready to challenge for a spot in African competitions next season.
Sekhukhune United coach Eric Tinkler is optimistic about his side's chances of securing a spot in next season's CAF Confederation Cup after moving to third in the Betway Premiership following a 2-1 victory over Cape Town City on Sunday.
