Cosmos slipped further down the table following their 5 - 0 loss to Orlando Pirates on Saturday, as they ended the weekend in 15th spot in the standings, just two ahead of bottom-placed Maritzburg United.
And Monare admits he and his teammates are worried, having hovered in and around the relegation zone all season.
"Remember that we've never moved away from the position that we were in (the relegation zone),” he said. “It's always been a concern … it's just that right now it got worse. We need to pull up our socks and just keep working hard and hope luck comes our way."
The midfielder believes things would have been different on Saturday if it wasn't for Chesslyn Jampies’s red card.
"I think we got the red card very early … and what do you expect when you are a man down, and playing an experienced side like Pirates? It has to be difficult, it as always going to be difficult."
Ezenkosi will be in for another tough time on Tuesday evening as they face another Soweto giant in Kaizer Chiefs, who will be looking to bounce back after three successive defeats.
And Monare is wary of the wounded Amakhosi.
"In Tuesday's game, we are also playing against a decent side and they have experience,” he said. “It's going to be a tough game, especially because Chiefs have lost three games in a row.
"Obviously they will want to turn the corner, but we will be up for it, and we will definitely pull up our socks."