Casric Stars overcame AmaZulu in their quarter-final tie, after seeing off Orlando Pirates in the previous round, as Milford defeated Sekhukhune United to secure their place in the last four.
Comitis paid tribute to both teams while also admitting his relief at being out of the competition as they focus fully on their return to the Betway Premiership.
City suffered a shock relegation last season but are in contention for an immediate return, in third place with 35 points from 19 games, just one point behind second-placed Milford FC and two adrift of National First Division leaders Kruger United.
The club chairman told Soccer Laduma: "Congratulations to the two NFD clubs. They're flying the flag for NFD quality and well done to them.
"We are extremely focused on the league situation. There is still a long way to go. And we take each game as it comes, one by one."
The Citizens exited the Nedbank Cup in their last of 32 qualifier to Upington City.
"We don't read anything into any of those Nedbank results at the end of the day. We've got to worry about ourselves. But on the back end, the fact that we don't have to be in the Nedbank is certainly a relief. Although it's always good to succeed in cup competitions. But in this instance, the focus has to be the league," Comitis added.
City are next in action against Milford at Athlone Stadium on Tuesday.
The draw for the semi-finals of the Nedbank Cup was conducted on Monday evening following the final round of quarter-final fixtures on Sunday that saw Durban City edge Golden Arrows.
Nedbank Cup quarter-final heroics saw Durban City coach Pitso Dladla turn to prayer during a tense penalty shootout against Golden Arrows on Sunday.
Eric Tinkler has dismissed suggestions that Sekhukhune United underestimated Milford following their dramatic exit from the Nedbank Cup on Saturday evening.
Durban City secured their place in the semi-finals of the Nedbank Cup with a 5-4 penalty shootout win over Golden Arrows on Sunday.
