Cech revealed it only took one win to spark the turnaround.
"The important one was the first one when we won the replay against Birmingham," he said. "That gave us confidence and got us through to the next round of the FA Cup.
"We followed it up by beating Stoke and we had two consecutive clean sheets.
"It gave us more confidence and obviously we wanted to show that we could play better than we were doing before.
"You can see everybody is trying to change things around and, suddenly, we're getting a bit of luck as well."