The Magpies, who have lost five games in a row, currently reside ninth in the Premier League table with three games left to play.
Only three points separate the North-East side from finishing the campaign in the bottom half of the standings.
"We are trying to win every game but our current form is not good enough," Chronicle Live quotes Coloccini as saying. "The fans are angry – we have to accept that. When you are not playing well, this is what happens."
The supporters have also vented their frustration at manager Alan Pardew, who will return to the touchline following a seven-match ban at the Emirates against Arsenal on Monday.