The Eagles face City on Sunday afternoon after recently beating Chelsea at Selhurst Park, but Dann insists that there will be no let-up whatever the opposition.
"We have kept ourselves in the division after people had written us off and it is a fantastic achievement. But now we have got a big say in what will go on at the top of the table," he told The Mirror.
"We have been on a good run recently and will not let our season fizzle out just because we are safe."
Palace host Liverpool at Selhurst Park next week.