Arsenal have won five, drawn once and not conceded in the Premier league since the hammering at Anfield.
'We said after the Liverpool game that the only way to bring everybody back on board was with our work attitude and the work ethic and the results and performances,' said Cech.
'We have been doing so, especially at home, and we feel like we have won the fans back onto our side and hopefully we can keep them happy as long as we can.'
The Gunners have won 11 in a row at the Emirates in all competitions, one short of equaling their record.
'It has always been our home,' Cech added. 'Obviously every fan has the right to show if he is not happy but as players we show the way and they support us home and away wherever we go. I think this is great to see.
'It was a big disappointment at Liverpool. The way we needed to respond was through our work and our results.
'Since then, we have been doing the work and when you get positive results the confidence of the team is back.'