Despite admitting that the squad is "buzzing" following that result, Cole hopes that they do not lose concentration in the coming months.
"Obviously the boys have been buzzing but it's important that we focus on the next game now," he told the club's official website.
"We had a team meeting and the gaffer knows that we have to do more if we want to stay in this league. We've set our targets now and all the boys know what we need to do to stay in it."
West Ham are back in action on Saturday when they travel to Aston Villa in the Premier League.