Highlands qualified for the quarter-finals of the cup after defeating Ernst Middendorp's charges on penalties at the Makhulong Stadium on Saturday.
"Ah, character hey, that's what I call character. The boys just showed the best character you could ask for, they really worked their socks off," Da Gama told SuperSport TV.
"You know they are a monkey on our back, Chiefs beat us twice this season and you know it was all about saying, "Guys, anything is possible, if you work hard and put everything into it, anything is possible".
"But I must give credit to Chiefs, they are a fantastic team you know maybe lady luck was a little bit on our side. I thought there were times where they could have snatched one. I thought there were times where we could have got one or two as well. But just the way the boys played, I think the character carried us through today, so we're very happy."
Da Gama added that there was an instruction to his players not to concede set-pieces in the last third but somehow Chiefs still managed to find those free-kicks in dangerous areas.
"There was a lot of concern because we said, 'Don't give those set-pieces away, don't give set-pieces away in the final third'. Chiefs are really dangerous with those types of set-pieces.
"But in saying that, I must give credit to Chiefs, they play very clever. They know how to get those free-kicks, that's something we gotta learn as well. So the referee was unbelievable, the linesman, there's nothing that you can take away from what happened in today's game.
"I just thought it was just a fantastic marvel of football to watch and we're happy for the fans, we're happy for the Chiefs fans. It kept everybody on their toes, from the start to finish, everybody was on their toes and I think it was a great advert for football. But from my side I was happy with the character the boys showed."