Spurs needed a late own goal from Emmerson Boyce to retrieve a point from the encounter despite Gareth Bale netting an early opener, after the relegation-threatened Latics took control for long periods of the match.
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"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," Parker told The Daily Mirror.
"But I don't think there is anything psychological happening in the changing room. I think we are showing character.
"I don't know what the stats are but apart from Manchester 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."
Tottenham are currently in fifth place and two points behind Arsenal, but have played one game fewer than the Gunners, while they are three points behind Chelsea who they are due to face next Wednesday.