Cardiff have spent close to £30million in the transfer market this summer but failed to trouble goalkeeper Jussi Jaaskelainen at any point as West Ham coasted to victory.
Allardyce believes the newcomers should look to Southampton, who made a poor start to their return to the Premier League last season, for comfort if results go against them.
"With the squad Cardiff have they'll hopefully get the results they're looking for. The challenge for them will be not getting too worried if they don't start well," he said.
"If it's to be your first game in the Premier League, you'd want it at home, not away. When we came up from the Championship we'd won more games away from home, but last season in the Premier League it was a huge task to pick up points away.
"Your home form is what you need to get right to stay in the Premier League."
Cole finished the opener beautifully, collecting a pass from Matt Jarvis, turning and skillfully directing the ball into the bottom right corner of the net. The 31-year-old was otherwise wasteful, although Allardyce stresses that it was his movement that put him in positions to score.
"Joe Cole's an England player, timing his runs and knowing where to run is what he's all about," he said. "To have the opportunity to get a hat-trick in the first 45 minutes, well his hardest chance was the one he scored from."