Spurs remain outside the top four following their 2-2 draw at Wigan this weekend, two points adrift of Arsenal and three behind Chelsea, although they have a game in hand on their bitter North London rivals.
Andre Villas-Boas' men needed a last-gasp own-goal from Emmerson Boyce to secure a point against the relegation-threatened Latics at the DW Stadium, with question marks raised over their mental toughness after previous failures.
The White Hart Lane club suffered a late-season slump last term to miss out on a place among Europe's elite, but Parker believes the resilience they have shown in recent fixtures demonstrates their strength of character.
"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," Parker said.
"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."