Arsenal have hit a purple patch since their humiliating 4-0 loss to Liverpool at the end of November.
They have not lost since then and enter the international break on the back of a 2-0 victory over Brighton, pushing them up to fifth place in the Premier League table.
Cech feels the Gunners' hard work has paid off and is looking forward to, rather than fearing, the November trip to the Etihad and December visit of United.
"We have still to play City and United, so there will be opportunities to get closer to them," said Cech.
"But we have responded well to the disappointing defeat at Liverpool.
"Everybody has been doing their job and the positive results have given us the confidence we need.
"We are playing better as a team. We're covering our mistakes with our hard work and the cohesion and defensive attitude is there. This is the way to go forward."