He believes Saturday's draw at struggling Wigan could turn out to be a vital point won rather than two dropped.
Midfielder Parker, 32, said: "People will always ask whether we can handle the pressure because of what happened in the past. But there is nothing psychological happening in the changing room. The fact that we missed out last season has never been mentioned.
"We are showing real character. Apart from Manchester United, we must be one of the best teams at coming back from losing positions. We are all a bit disappointed but at 2-1 down with a couple of minutes to go it could be a big point for us really.
"I'm sure other teams will be dropping points as well and we have to go to Chelsea on Wednesday week. That could be the decider really. It looks like that game is going to be a pivotal one.
"But I am sure there will be some more twists and turns like we always see at the end of the season in this league."