Parker thinks that his side possess enough character and quality to take advantage of any slip-ups from the Gunners or Chelsea in the final weeks of the campaign.
He told The Mirror: "I think people will always ask whether we can handle the pressure and put those questions to us because of what happened in the past, but I don't think there is anything psychological happening in the changing room," said the England midfielder.
"I think we are showing character. I don't know what the stats are but apart from Man United, I think we might be one of the best teams at coming back from losing positions. We have got great character and great belief here. It was massive with a couple of minutes to go to get back and we tried to nick it at the end.
"We have to take the positives. We are all disappointed at the moment, but in a couple of days we will get back focused on what we need to do. There are four games left and along the way we need to pick up as many points as we can. I'm sure along the way other teams will be dropping them as well so this could be a big point."
Andre Villas-Boas's side host Southampton next weekend before a crunch clash with Chelsea at Stamford Bridge on May 8.