Alan Pardew's side secured only their second win in 10 games last Sunday, Loic Remy's last-gasp winner ensuring a 1-0 victory over Aston Villa that ended a run of five straight defeats at St James' Park.
Newcastle are eighth in the Premier League following that triumph, but are well adrift of the European places and are out of both domestic cup competitions.
However, skipper Coloccini, who returned from a knee injury to help Newcastle defeat Paul Lambert's men, is adamant that he and his team-mates are full of motivation for their remaining 11 games.
"People might say there is not a lot to play for in the rest of the season, but that is not correct," Coloccini told The Northern Echo.
"It is never a problem to get motivated when you are playing for a club like this.
"All of us in the dressing room know about Newcastle's history, and we know we are playing for one of the biggest clubs in the country. That is what we are fighting for when we go on the pitch.
"The biggest motivation is knowing that you are representing Newcastle and the Newcastle fans. When you think about the 52,000 fans who come here to support us, you know you have to go out and give your all.
"We know we have been in some bad times. It has not been easy for the fans or the whole of the city.
"The mood has been a little bit sad because of some bad results, so we knew the game against Aston Villa was going to be a massive one, and the three points are very important for us.
"There had been a few games where we hadn't been able to get the three points, so it was important to stop that. Now, we have to start looking forward.
"There are still plenty of games to play, and as long as we show the same fighting spirit we did against Villa, we should do well in them."
