Wiseman Meyiwa was given his marching orders for a challenge on Daine Klate, and Wits took full advantage of the situation as they scored through James Keene minutes later.
While Chiefs responded well in the second half, they missed too many goalscoring chances, which Komphela felt they should have easily converted.
Komphela feels his side, despite being one man short, did put in enough effort to match the Students throughout.
"I thought the first half we didn't do well and obviously the red card we conceded changed dimensions," Komphela told SuperSport after the game.
"The second half was better. We created more chances and we spent more time on their half than ours. It's just unfortunate that we have to lose matches of this calibre, but again the lesson we've learned is that the mistakes we make are very crucial we cannot afford that," he said.
"You had to be positive, you're losing, it's a knockout competition. You had to make a choice; you compromise one of the defenders I thought it worked well. Even when we suffered one man we could have scored here, the chance that Zuma had when he hit the crossbar and the one where he clashed with the goalkeeper. In matches of this calibre you have to take one of them," he added.
"If you're one man down, in a game of 10 people and there's 10 available then it means each one of us has to give an extra 10 percent so we can complete the eleven on the field. So, we need to create an extra player by effort. We did and it worked, I think the players did well to create that additional player we lost," said Komphela.