The Hammers beat Newcastle 2-0 on, and looked a class above Steve McClaren's side on the night, but Coloccini insists that the two sides are in the 'same league'.
The Magpies defender also suggests that Newcastle's next opponents, Watford, are a team which they should be taking points off.
"We see games against West Ham and Watford as teams in 'our league' who we should be taking points from so it's disappointing," he said.
"We must try to avoid the same mistakes going forward. For us, we can't afford to have our heads down so we must look forward and get some points. We need to eliminate the mistakes and learn from it."
At the moment, West Ham are in fifth place in the Premier League, whereas Newcastle are propping up the table, but Coloccini clearly has ambitions of rivalling the London club by the end of the season.
If the Magpies are to do that, they will have to improve considerably, as so far this campaign they have appeared to be off the pace.
Newcastle have struggled to create chances and they are still looking for their first win of the new season, having picked up just two points so far.
Watford, meanwhile, are in 13th place and travel to St. James' Park at the weekend having just picked up their maiden win of the new campaign - after beating Swansea City 1-0 in their most recent outing.