The Rockets made it to the last eight with 1-0 victory over Orbit College where the match also went to extra time before substitute Mehdi Ouamri was able to finish from close-range.
This time Galaxy found themselves a goal up early on from a Sibonelo Cele own-goal in the 19th minute before conceding in similar fashion as MacBeth Mahlangu put the ball through his own net at the other end, in the 44th minute.
Nqobeko Dlamini proved to be the match-winner for Manqoba Mngqithi's charges at the King Zwelithini Stadium with his goal in the 99th minute.
Reflecting on the tie, Beganovic, who's team are in eighth place on the Betway Premiership standings after nine games of the new season, admitted that he doesn't have the squad depth to compete on more than one front.
He said on IOL: "It's very tricky for the small clubs with small squads like us. It's important to understand how difficult it is to play on all fronts with the league and all the domestic cups.
"Everyone knows we started the season with 14 players and we had to include players from our reserve team.
"We only had about two or three subs on the bench — it wasn't easy.
“Even when we did register players, it's not easy having to get everyone on the same level in terms of fitness. That's what we're trying to work on now."
Galaxy are next in action at home against Stellenbosch in the league on Sunday.
Mamelodi Sundowns head coach Miguel Cardoso hit out his side's hectic fixture schedule as the reason for their season defining 3-2 defeat to TS Galaxy on Tuesday.
TS Galaxy interim coach Bernard Parker admits that Mamelodi Sundowns succumbed to the pressure of needing a win from their last Betway Premiership match of the season.
Mamelodi Sundowns' bid to pull clear at the top of the Betway Premiership suffered a major setback on Tuesday night after they were beaten 3-2 by TS Galaxy at Mbombela Stadium, a result that dramatically reshapes the title race.
Mamelodi Sundowns head into their final league match of the season knowing their dominance of South African football could finally be coming to an end.
