The Black Cats conceded two points late on after drawing 2-2 at Reading.
Sunderland fell behind to a 20th minute Liam Kelly penalty after Lee Camp's error, bringing down Jon Dadi Bodvarsson inside the area but they fought back well in the second half.
A stunning Paddy McNair strike was followed by Lee Cattermole's close-range header but the Black Cats couldn't hold on to what would have proved a huge three points.
Instead, sub Yann Kermorgant denied them all three points when he headed in a Chris Gunter cross 11 minutes from time to leave Sunderland bottom after Burton Albion beat Derby County.
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Sunderland are six points adrift with just three games to play, while rivals Barnsley - who rescued a point at fourth-bottom Bolton Wanderers with a stoppage time equaliser - have a game in hand.
It could have been a different story had they managed to hold on to leads in their last three games, only to draw with Leeds United and Norwich as well as today.
Coleman said: "Three games running we have dropped points. We have done enough in games to earn all three points but given it up.
"Obviously it is critical for us at this stage of the season.
"The performance and the mentality was spot on, brilliant, but it is those fine details we haven't taken care of, all season really.
"1-0 down, to go 2-1 up, we haven't done that too many times this season and I can't say we were ever in too much difficulty.
"At that stage when it was 2-1, if anything we were going to score again. In fairness it was a great cross and header from Kermorgant.
"It is disappointing because we have given it up again.
"It is the traits of a team that has been down there a long time, in those final moments, those real pressurised moments in games when you can deal with it, we get that feeling of 'are we going to get punished?' And we do get punished.
"It is those fine details that have let us down. Their attitude was fabulous, not much more I could ask in terms of their input in the game."