The Urban Warriors have now gone eight games without a win in all competitions and they are the only club without a league win in 2017 after Baroka FC shocked title contenders SuperSport United yesterday.
Menzo, who took over from Roger de Sa, said he's starting to get concerned about the club failing to get a win as other teams close to them in the standings are picking up points.
"You [the media] don't have to get worried but I've got to get worried and as coach I've to get worried and yes we are concerned," Menzo told reporters after the game.
"If you look at this game I think we were the better team, we had the better chances only we had to score the goals and don't concede chances and goals like that.
"I think they had one chance in the first [which they scored] and that's all.
"In the second-half they had two chances and the goal they scored was [from] the free-kick in the set piece at the end where we were pressing they scored as well on the counter attack that was all."
Menzo, who is coaching for the first time in the PSL, was defiant when asked whether he still has control of the dressing room.
"What do you mean they [players] are still on my side? It's question I think, you saw the whole game so didn't they respond, yes or no? I think they did respond. For me they didn't play badly but they didn't play well either.
"When you don't play well don't give it [the ball] away because we had the chances and don't give it away so easily.
"I'm worried yes but I'm fighting and I'm a fighter and I'll keep on fighting."
The Urban Warriors are 12th on the table with 22 points from 20 matches. Highlands Park, who are also struggling at the moment, will be their visitors on April 12 at Cape Town Stadium.