Boss Sam Allardyce says Sunderland must "accept" they are among the favourites for relegation from the Premier League after their draw at Southampton.
A 93rd-minute equaliser from 10-man Southampton leaves Sunderland one point and one place above the drop zone.
"We have shot ourselves in the foot," Allardyce told BBC Newcastle.
"What a massive difference it makes to our plight at this stage of the season. We should be going three points clear of the bottom three."
Jermain Defoe scored his 14th goal of the season to give Sunderland the lead at St Mary's, but a stoppage-time leveller from Virgil van Dijk denied the Premier League strugglers maximum points.
The Black Cats are above Norwich, who are in the last relegation spot, while Newcastle are also a point adrift of their north-east rivals, but have a game in hand.
"It's going to take some getting over for me," Allardyce continued.
"Don't keep saying we're out the bottom three - it's not enough points. We've got to accept that we're still one of the favourites to get relegated."
He continued: "There's no game [for Sunderland] next week which means nobody could have caught us up if they win - now they could go past us and that puts extra pressure on us."
Allardyce's side will next play Newcastle at St James' Park on Sunday, 20 March in what could be a decisive derby clash.
"We have got a crucial game at Newcastle in two weeks and this one will make the difference for me," said defender Younes Kaboul.
"We have to make sure we are ready to give everything for the fans."