Leonardo Castro came off the bench to score the winner soon after Joseph Molangoane was sent off for an off-the-ball incident.
"We had to [dig deep] even with the red card, we had to keep the calm heads; you can't lose it. We just needed to have a slight tweak without being obvious to what we are doing," Komphela told SuperSport TV.
The 50-year-old was happy with the performances of Ryan Moon and Castro, who both found the back of the net on the day, and although Chiefs walked away with all the points on offer, Komphela feels the overall performance of the team could have been better.
"I'm happy for Leo; a great goal he scored. I'm happy for Moon; a great goal he scored as well, but I thought the overall performance could have been better," he said.
"I think we're giving away possession easily. Too much turn-overs and when you're playing a team like Baroka, who are waiting for you to make that technical error and they pounce, we played into their hands; we shouldn't do that. Good victory, good points. We're happy. We need points at this stage of the season although there's still a number of things that I felt we could have done better," added Komphela.
Quizzed about his thinking behind making certain substitutions, especially after Dumisani Zuma, Siphelele Ntshangase and Castro turned the tie on its head, Komphela said: "Life is challenging that you still remain rational while the emotions are constantly hitting you. You need to think it through [and] not let the heart take charge. I thought the subs were timeous and they did make the difference. Leo's difference is clear, Zuma's difference is clear. I think Ntshangase will get to the level where both going forward and coming back to defend become part of his game."
With Molangoane set to miss the next two matches through suspension, Komphela sees this as an opportunity for other players to come in and show what they can offer the team.
"We'll be missing 'Tight', but it's an opportunity for someone to come in and showcase," concluded the Amakhosi mentor.