The Welsh outfit pulled off a shock victory at the Stoop on Saturday to earn a 33-26 win at the home of the Aviva Premiership side.
"I'm delighted with the way we went about our business," Easterby told reporters. "It's vital that you win your home games in the Heineken Cup and if you can get points on the road then that's a big advantage.
"But this won't mean anything we don't get a result at home nest weekend. This was a big performance but we have to keep our feet on the ground."
Scarlets host Racing Metro next weekend in the cup.