Disappointing recent defeats at struggling Southampton and Norwich in the last four games have slightly taken the gloss off their previous 13-match unbeaten run.
But Parry is adamant the Bluebirds, who lie nine points adrift of second-placed Birmingham with three games in hand, can still be in the top two come May 3.
"We still feel an automatic place is there for the taking," the midfielder told the South Wales Echo. "Most of the teams around us drew in the week which, in a way, made the result at Norwich a little bit more disappointing because we missed out on the chance of making up some ground.
"It feels like another opportunity passed us by. It will be the teams who hold their nerve in there now, who put a run of results together, who will be going up at the end of the season. We want to be one of them, of course."
He added: "What we need to do is make one final big push. We've only lost six games all season, but we need to put a bit of a run together again now and put ourselves in a good position. It really is up to us in many ways how this season is going to finish for us."