The Hammers have accumulated 47 points so far and Cole is hoping that they can collect at least one more victory before the campaign comes to a close.
West Ham have three fixtures remaining - against Aston Villa, Everton and Newcastle United - and their objective during the run-in is clear.
"Put simply, we want to get as high as we can and try to get as many points as possible and get our personal goals ticked off," said Cole.
"We want to get the most amount of points that this team has ever got since promotion. We’ve now beaten our previous best of 46 points but now we need to get to the 50s."
West Ham may have beaten their total from the last campaign, but it is hard to imagine that this season, ultimately, will be considered anything other than a disappointment.
A mid-table finish is a decent showing from the side, but it could have been so much better if they had been able to maintain any sort of form.
Sam Allardyce has seen results dip dramatically after Christmas, with a run of just three wins in 17 matches seeing frustration levels build around Upton Park.
The Hammers have tumbled from being a side that appeared capable of competing for a European spot into one that is struggling to cement a top-half standing, and it is this inconsistency which may end up costing Allardyce his job, with the experienced manager's contract set to expire in the summer.