The Magpies held crisis talks with manager John Carver earlier this week after losing their last eight league matches - their worst run since 1977.
They are now two points above the relegation zone with three games left.
"On behalf of the squad we would like to apologise for the moment we are going through," wrote Coloccini.
"Players and staff have come together in order to leave all past problems aside and to focus 100% on the three 'cup finals' that we have left.
"I would like to make a call to all fans today to also leave aside all differences, all different opinions, anything that divides us as people who love this club."
Newcastle host West Brom on Saturday before travelling to QPR on 16 May and then hosting West Ham on 24 May.
"The time we have left to turn around this situation is short but after the end of the season we will try to learn from the mistakes we made so that we don't have to go through this again," added Coloccini.
"This is as painful for us as it is for you, because when this team comes onto the pitch we do so with the intention of winning and to defend not just the colours of this club, not just our shirt, but also to represent thousands of fans, the whole city."
Carver's position came under fresh scrutiny after he accused defender Mike Williamson of deliberately getting himself sent off in Saturday's 3-0 defeat by fellow strugglers Leicester City.
However, the club issued a statement insisting he was staying.
BBC Sport understands Derby County boss Steve McClaren was asked to take over for the final three games but turned the job down.

People living close to the plant in Monkton Lane, Farnham, have complained that the stench has recently got worse.
Thames Water, which manages the site, said emergency repair work could be the cause, but that it had written to residents to explain the situation.
Local councillor Roger Steel said he had been inundated with complaints, but the firm said it was not aware of any.
He said the Farnham Sewage Treatment Works was built 100 years ago and the odour problem was not new.
"In the summer residents are not able to open the windows when it's hot, children can't play in the garden.
"The odour gets into their clothes, even the wallpaper," Mr Steel said.
The councillor, who represents Farnham Moor Park on Waverley Borough Council, said the plant was too old to cope with the current population it served.
"There's plenty of room for them to perhaps rebuild a new plant or even to make major additions for it to be able to cope.
"It's been inadequate for years and years and years," he said.
In a statement, Thames Water said: "We're sorry if residents have noticed an increase in odour, but we're not aware of any complaints and [have] not noticed any difference.
"We sent a courtesy letter to inform residents we would be doing a piece of cleaning work, outside of day-to-day operations.
"Work stated last Tuesday, and is going well - we're ahead of schedule."
Newcastle United captain Fabricio Coloccini has written an open letter to fans calling for unity as the club battles to stay in the Premier League.
[NEXT_CONCEPT]
Residents in a Surrey town have claimed their lives are being made a misery due to the smell from nearby sewage works.