Elliot came into the side after first-choice goalkeeper Tim Krul went down to a season-ending knee injury and had to overcame a thigh injury of his own to be fit for Saturday.
After a 0-0 draw against Stoke in their previous league game, Elliot now has back-to-back clean sheets, a first for Newcastle this season.
The win, just Newcastle's second in the Premier League, saw them climb out of the bottom three to 17th, with Bournemouth taking their place in the relegation zone.
"We need people like Robbie, with his strong character, in this dressing room," Coloccini told the club's website (www.nufc.co.uk).
"He never lets us down and when things are not going well he will not hide.
"Last week he played with an injury and was strong and played for the team," the Argentine added.
Coloccini admitted Newcastle were fortunate to grab their first away win since January but was confident they could escape relegation.
"The three points was all that mattered. In the game, we didn't play well and maybe didn't deserve to win, because they created a lot of situations.
"But this is football. We defended well, like a team, and kept a clean sheet. At the other end we took our chance, so it was very positive.
"We know we are going the right way and the results are starting to show that," he said.
Bournemouth boss Eddie Howe rued his side's inability to convert possession into goals.
"The disappointing part for us was that we didn't capitalise on our really good spell," he told the club's website (www.afcb.co.uk).
"For 70 minutes of the game we really were terrific. We dominated the ball and dominated chances, so it's hugely frustrating not to win let alone lose the game.
"We created a number of chances and we just didn't take them," he added.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Peter Rutherford)
